Papers
Submitted:
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A.R. Polavarapu, and V.G. Troitsky,
A representation of sup-completion.
arXiv.
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T. Oikhberg, M.A. Taylor, P. Tradacete, and V.G. Troitsky,
Free Banach lattices.
arXiv.
Papers in refereed journals:
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E. Bilokopytov and V.G. Troitsky,
Uniformly closed sublattices of finite codimension.
Linear and Multilinear Algebra,
to appear.
arXiv.
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E. Bilokopytov and V.G. Troitsky,
Order and uo-convergence in spaces of continuous functions.
Topology and Appl.,
308, 2022.
doi,
arXiv.
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M.O'Brien, V.G. Troitsky, and J.H. van der Walt,
Net convergence structures with applications to vector lattices.
Quaestiones Math.,
46(2), 2023.
doi,
arXiv.
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H. Jardón-Sánchez, N.J. Laustsen, M.A. Taylor, P. Tradacete, and V.G. Troitsky,
Free Banach lattices under convexity conditions.
Revista R. Acad. Cienc. Exactas (RASCAM),
116(15), 2022.
doi,
arXiv.
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M.A. Taylor and V.G. Troitsky,
Bibasic sequences in Banach lattices.
J. of Functional Analysis,
278(10), 2020, 108448.
doi,
PDF,
arXiv.
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N.J. Laustsen and V.G. Troitsky,
Vector lattices admitting a positively homogeneous continuous function calculus.
Quarterly J. Math.,
71(1), 2020, 281-294.
doi,
journal,
PDF,
arXiv.
More info.
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V.G. Troitsky,
Simple constructions of FBL(A) and FBL[E].
Positivity, 23(5), 2019, 1173-1178.
doi,
PDF,
arXiv,
readcube.
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V.G. Troitsky, M.S. Türer,
Krivine's Function Calculus and Bochner integration,
Canadian Math. Bull.,
62(3), 2019, 663-669.
doi,
PDF,
arXiv.
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M. Kandić, H. Li, and V.G. Troitsky,
Unbounded norm topology beyond normed lattices,
Positivity,
22(3), 2018, 745-760.
doi,
PDF,
arXiv,
readcube.
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M. Kandić, M.M.A. Marabeh, and V.G. Troitsky,
Unbounded norm topology in Banach lattices,
J. Math. Analysis and Appl.,
451(1), 2017, 259-279.
PDF,
doi,
arXiv.
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H.G. Dales, N.J. Laustsen, T. Oikhberg, and V.G. Troitsky,
Multi-norms and Banach lattices,
Dissertationes Mathematica, 524, 2017, 1-115.
PDF,
doi.
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Y. Deng, M. O'Brien, and V.G. Troitsky,
Unbounded norm convergence in Banach lattices,
Positivity,
21(3), 2017, pp 963-974.
PDF,
doi,
readcube,
arXiv.
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N. Gao, F. Xanthos, and V.G. Troitsky,
Uo-convergence and its applications to Cesàro means in Banach lattices,
Israel J. Math.,
220, 2017, 649-689.
PDF,
arXiv,
doi,
readcube.
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S. Adeeb and V.G. Troitsky,
Locally piecewise affine functions and their order structure,
Positivity,
21(1), 2017, 213-221.
arXiv,
doi,
readcube.
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F. Xanthos and V.G. Troitsky,
Spaces of regular abstract martingales,
J. Math. Analysis and Appl.,
434(2), 2016, 1753-1761.
arXiv,
doi.
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J. Flores, F.L. Hernandez, E. Spinu, P. Tradacete, and V.G. Troitsky,
Disjointly homogeneous Banach lattices: duality and complementation,
J. of Functional Analysis,
266(9), 2014, 5858-5885.
PDF,
doi.
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O. Zabeti and V.G. Troitsky,
Fremlin tensor products of concavifications of Banach lattices,
Positivity,
18(1), 2014, 191-200.
PDF,
arXiv,
doi.
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N. Gao and V.G. Troitsky,
Irreducible semigroups of positive operators on Banach lattices,
Linear and Multilinear Algebra,
62(1), 2014, 74-95.
PDF,
arXiv,
doi.
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Q. Bu, G. Buskes, A.I. Popov, A.Tcaciuc, and V.G. Troitsky,
The 2-concavification of a Banach lattice equals the diagonal of the Fremlin tensor square
Positivity,
17(2), 2013, 283-298.
PDF,
doi.
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V.G. Troitsky,
A remark on invariant subspaces of positive operators.
Proceedings of the Amer. Math. Soc.,
141, 2013, 4345-4348.
PDF,
doi.
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A. Kaminska, A.I. Popov, E. Spinu, A. Tcaciuc, and V.G. Troitsky,
Norm closed operator ideals in Lorentz sequence spaces,
J. Math. Analysis and Appl.,
389(1), 2012, 247-260.
PDF,
arXiv,
doi.
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V. Galvani and V.G. Troitsky,
Options and Efficiency in Spaces of Bounded Claims,
J. of Math. Economics,
46(4), 2010, 616-619.
PDF,
doi.
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H.E. Gessesse and V.G. Troitsky,
Martingales in Banach lattices, II,
Positivity,
15(1), 2011, 49-55.
PDF,
doi.
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V.G. Troitsky,
When are the nonstandard hulls of normed lattices discrete or continuous?
Vladikavkaz Math. J.,
11(2), 2009, 43-45.
PDF.
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H.E. Gessesse, A.I. Popov, H. Radjavi, E. Spinu, A.Tcaciuc, and V.G. Troitsky,
Bounded indecomposable semigroups of non-negative matrices,
Positivity,
14(3), 2010, 383-394
PDF,
doi.
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G. Androulakis, A.I. Popov, A.Tcaciuc, and V.G. Troitsky,
Almost invariant half-spaces of operators on Banach spaces,
Integral Equations and Operator Theory,
65(4), 2009, 473-484.
PDF,
doi.
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J. Flores, P. Tradacete, and V.G. Troitsky,
Disjointly homogeneous Banach lattices and compact products of operators,
J. Math. Analysis and Appl.,
354, 2009, 657-663.
PDF,
doi.
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A. Popov and V.G. Troitsky,
A version of Lomonosov's theorem for collections of positive operators,
Proceedings of the Amer. Math. Soc.,
137, 2009, 1793-1800.
PDF,
doi.
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I. Chalendar, E. Fricain, A. Popov, D. Timotin, and V.G. Troitsky,
Finitely strictly singular operators between James spaces,
J. of Functional Analysis,
256(4), 2009, 1258-1268.
PDF,
doi.
More info.
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J. Flores, P. Tradacete, and V.G. Troitsky,
Invariant subspaces of positive strictly singular operators
on Banach lattices,
J. of Math. Analysis and
Applications,
343, 2008, 743-751.
PDF,
doi.
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V.I. Lomonosov, H. Radjavi, and V.G. Troitsky,
Sesquitransitive and localizing operator algebras,
Integral Equations and Operator Theory,
60(3), 2008, 405-418.
PDF,
doi.
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H. Gessesse and V.G. Troitsky,
Invariant subspaces of positive quasinilpotent operators on
Banach spaces with generating closed cones,
Positivity,
12(2), 2008, 193-208.
PDF.
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G. Androulakis, P. Dodos, G. Sirotkin, and V.G. Troitsky,
Classes of strictly singular operators
and their products,
Israel J. Math., 169(1), Jan 2009, 221-250.
PDF,
doi
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B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann, and V.G. Troitsky,
On norm closed ideals in
L(lp+lq),
Studia Math.,
179, 2007, 239-262.
PDF.
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H. Radjavi and V.G. Troitsky,
Invariant sublattices,
Illinois J. Math., 52(2), 2008, 437-462.
PDF.
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H. Radjavi and V.G. Troitsky,
Semitransitive spaces of operators,
Linear and Multilinear Algebra, 57(1), Jan 2009, 1-11.
PDF.
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Yu.A. Abramovich, C.D. Aliprantis, G. Sirotkin, and V.G. Troitsky,
Some open problems and conjectures associated
with the Invariant Subspace Problem,
Positivity,
9(3), 2005, pp 273-286.
PDF.
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J. Bernik, L. Grunenfelder, M. Mastnak, H. Radjavi, and V.G. Troitsky,
On semitransitive collections of operators,
Semigroup Forum,
70(3), 2005, 436-450.
PDF.
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R. Anisca and V.G. Troitsky,
Minimal vectors for positive operators,
Indiana University Math. J.,
54(3), 2005, 861-872.
PDF.
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V.G. Troitsky,
Martingales in Banach lattices,
Positivity,
9(3), 2005, 437-456.
PDF.
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H. Rosenthal and V.G. Troitsky,
Strictly semi-transitive operator algebras,
J. of Operator Theory,
53(2), 2005, 315-329.
PDF.
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T. Oikhberg and V.G. Troitsky,
A theorem of Krein revisited,
Rocky Mountain J. Math.
35(1), 2005, 195-210.
PDF.
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V.G. Troitsky,
On CD0(K)-spaces,
Vladikavkaz Math. J.,
6(1), 2004, 71-73.
PDF.
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V.G. Troitsky,
Minimal vectors in arbitrary Banach spaces,
Proceedings of the Amer. Math. Soc.,
132, 2004, 1177-1180.
More info,
PDF.
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V.G. Troitsky,
Measures of non-compactness
of operators on Banach lattices,
Positivity,
8(2), 2004, 165-178.
PDF.
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S.J. Dilworth and V.G. Troitsky,
Spectrum of a weakly hypercyclic
operator meets the unit circle,
Trends in Banach Spaces and Operator Theory
in Contemporary Mathematics,
AMS, vol 321, 2003, 67-69.
PDF.
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Th. Schlumprecht and V.G. Troitsky,
On quasi-affine transforms of Read's operator,
Proceedings of the Amer. Math. Soc.
131, 2003, 1405-1413.
PDF.
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V.G. Troitsky,
Spectral radii of bounded operators on topological vector
spaces,
PanAmerican Math. J.
11(3), 2001, 1-35.
PDF.
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V.G. Troitsky,
Lomonosov's theorem cannot be extended
to chains of four operators,
Proceedings of the Amer. Math. Soc.,
128, 2000, 521-525.
More info,
PDF.
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V.G. Troitsky,
Infinitely fine partitions of measure spaces,
Vladikavkaz Math. J.,
1(3), 1999, 53-59.
More info,
PDF.
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V.G. Troitsky,
On the modulus of C.J. Read's operator,
Positivity,
2(3), 1998, 257-264.
More info,
PDF.
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V.G. Troitsky,
Real partitions of measure spaces,
Siberian Math. J.,
35(1), 1994, 189-191.
More info, download.
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V.G. Troitsky,
Nonstandard discretization and the Loeb
extension of a family of measures,
Siberian Math. J.,
34(3), 1993, 566-573.
More info, download.
Other publications
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Invariant subspace problem and spectral properties
of bounded linear operators on Banach spaces, Banach lattices,
and topological vector spaces,
Ph.D. Thesis, 1999.
More info,
PDF.
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A proof of Frobenius theorem,
unpublished, 1997.
More info.
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On some problems of nonstandard measure theory,
Master Thesis, 1993.
More info, download.