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# Mikhail Ostrovskii

**Educational Background**

Habilitation Degree, 1998, Institute for Low Temperature Physics, Mathematics

Ph. D., 1985, Supreme Attestation Committee of the U.S.S.R, Mathematics

Calculus with Business Applications

Computer Algorithms

Differential Equations

Discrete Mathematics

Linear Algebra

Mathematics for Liberal Arts

Statistical Applications for Pharmacy and Allied Health

Theory of Functions of a Complex Variable I and II

University Calculus I, II, and III

(An updated list of publications can be found at http://facpub.stjohns.edu/ostrovsm/.)

Compositions of projections in Banach spaces and relations between approximation properties, Rocky Mountain Journal of Mathematics, to appear.

Operator quadratic inequalities and linear fractional relations (with V.A. Khatskevich and V.S. Shulman), Functional Analysis and its Applications, to appear.

Analogues of the Liouville theorem for linear fractional relations in Banach spaces (with V.A. Khatskevich and V.S. Shulman), Bulletin of the Australian Mathematical Society, 73

(2006), 89-105.

Sobolev spaces on graphs, Quaestiones Mathematicae, 28 (2005), 501-523.

Linear fractional relations for Hilbert space operators (with V. A. Khatskevich and V. S. Shulman), Mathematische Nachrichten, 279 (2006), 875-890.

Minimal congestion trees, Discrete Math., 285 (2004) 219-226.

Finite dimensional characteristics related to superreflexivity of Banach spaces, Bulletin of the Australian Mathematical Society, 69 (2004) 289-295.

Extremal problems for operators in Banach spaces arising in the study of linear operator pencils, II, Integral Equations and Operator Theory, 51 (2005) 553-564.

Sufficient enlargements of minimal volume for two-dimensional normed spaces, Mathematical Proceedings of the Cambridge Philosophical Society, 137 (2004), 377-396.

Extremal problems for operators in Banach spaces arising in the study of linear operator pencils (with V. A. Khatskevich and V. S. Shulman), Integral Equations and Operator Theory, 51 (2005), 109-119.

Minimal volume projections of cubes and totally unimodular matrices, Linear Algebra and its Applications, 364 (2003), 91-103.

A new class of normed spaces with non-trivial groups of isometries and some estimates for operators with given action, Rocky Mountain Journal of Mathematics, 34 (2004), no. 1, 59-81

(with B. L. Chalmers).

Paths between Banach spaces, Glasgow Math. J., 44 (2002), 261-273.

Hahn-Banach operators, Proc. Amer. Math. Soc., 129 (2001), 2923-2930.

Weak* sequential closures in Banach space theory and their applications, in: "General Topology in Banach Spaces", ed. by T. Banakh and A. Plichko, Nova Sci. Publ., Huntington, New York, 2001, pp. 21--34.

Minimal-volume shadows of cubes, J. Funct. Anal, 176 (2000), no. 2, 317--330.

Hahn-Banach operators: a review, J. Comput. Anal. Appl., 5 (2003), no. 1, 11-24 (with B. L. Chalmers and B. Shekhtman).

A short proof of the result on actions that characterize $l_\infty^n$, Linear Algebra and its Applications, 294 (1999), 193--195, MR2000d:46016.

Completions with respect to total nonnorming subspaces, Matematicheskaya Fizika, Analiz i Geometriya, 6 (1999), no. 3/4, 317--322.

Projections in normed linear spaces and sufficient enlargements, Archiv der Math., 71 (1998), no. 4, 315—324.

Generalization of projection constants: sufficient enlargements, Extracta Math., 11 (1996), no. 3, 466--474.

Distances between Banach spaces, Forum Math., 11 (1999), 17-48, (with N. J. Kalton).

On prequojections and their duals, Revista Mat. Univ. Complutense Madrid, 11 (1998), 59-77.

On norming Markushevich bases, Mat. Stud., 5 (1995), 39—42.

Classes of Banach spaces stable and unstable with respect to the opening, Quaestiones Math., 19 (1996), no. 1-2, 191—210.

Quojections without Banach subspaces, Bull. Pol. Acad. Sc., 44 (1996), no. 2, 143—146.

Operator ranges in Banach spaces, I, Math. Nachr., 173 (1995), 91-114 (with R. W. Cross and V. V. Shevchik).

Topologies on the set of all subspaces of a Banach space and related questions of Banach space geometry, Quaestiones Math., 17 (1994), no. 3, 259-319.

On complemented subspaces of sums and products of Banach spaces, Proc. Amer. Math. Soc., 124 (1996), no. 7, 2005—2012.

A note on continuous restrictions of linear maps between Banach spaces, Acta Math. Univ. Comenianae, 61 (1992), no. 2, 185-188.

A note on analytical representability of mappings inverse to integral operators (Russian), Matematicheskaya Fizika, Analiz i Geometriya, 1 (1994), no. 3/4, 513-519.

Total subspaces with long chains of nowhere norming weak* sequential closures, Note Mat., 13 (1993), no. 2, 217-227.

Characterizations of Banach spaces which are completions with respect to total nonnorming subspaces, Archiv der Math., 60 (1993), 349-358.

On the classification of total subspaces of dual Banach spaces, C. r. Acad. bulg. Sc., 45 (1992), no. 7, 9-10.

The structure of total subspaces of dual Banach spaces (Russian), Teor. Funktsii, Funktsional. Anal. i Prilozhen. 58 (1992), 60-69.

Total subspaces in dual Banach spaces which are not norming over any infinite-dimensional subspace, Studia Math. 105 (1993), no. 1, 37-49.

Subspaces containing biorthogonal functionals of bases of different types (Russian), Teor. Funktsii, Funktsional. Anal. i Prilozhen. 57 (1992), 115-127; English transl.: J. Math. Sci., 77

(1995), no. 1, 3008-3016.

Regularizability of inverse linear operators in Banach spaces with bases (Russian), Sibirsk. Mat. Zh. 33 (1992), no 3, 123-130; English transl.: Siberian Math. J. 33 (1992) no. 3, 470-476.

On the support of the Riesz charge of a δ-subharmonic function (Russian), in: “Operator theory, subharmonic functions” (ed. by V. A. Marchenko), Kiev, Naukova Dumka, 1991, pp. 50-54, MR93j:31002, (with A. E. Eremenko and M. L. Sodin).

On the problem of regularizability of the superpositions of inverse linear operators (Russian), Teor. Funktsii, Funktsion. Anal. i Prilozhen. 55 (1991), 96-100; English transl.: J. Soviet Math. 59 (1992), no. 1, 652-655.

On one-side invertible operators (Russian), in: “Analytical methods in probability and operator theory” (ed. by V. A. Marchenko), Kiev, Naukova dumka, 1990, p. 95-105.

Operators with dense range and extensions of minimal systems (Russian), Izvestiya vuzov, Matem., 1990, no. 6, 45-47; Engl. transl.: Soviet. Math. (Iz. VUZ) 34 (1990), no. 6, 53-56 (with V. P. Fonf).

Basic and quasibasic subspaces of dual Banach spaces (Russian), Mat. Zametki 47 (1990), no. 6, 85-90; Engl. transl.: Math. Notes 47 (1990), no. 5-6, 584-588.

On total non-norming subspaces of a dual Banach space (Russian), Teor. Funktsii, Funktsion. Anal. i Prilozhen. 53 (1990), 119-123; Engl. transl.: J. Soviet Math. 58 (1992), no. 6, 577-579.

Comparison of topologies generated by geometric and operator gaps between subspaces (Russian), Ukr. Mat. Zh. 41 (1989), no. 7, 929-933; Engl. transl.: Ukr. Math. J. 41 (1989), no. 7, 794-797.

Total property of bounded approximation (Russian), Sibirsk. Mat. Zh. 30 (1989), no. 3, 180-181; Engl. transl.: Siberian Math. J. 30 (1989), no. 3, 488-489.

Pairs of regularizable inverse linear operators with nonregularizable superpositions (Russian), Teor. Funktsii, Funktsion. Anal. i Prilozhen. 52 (1989), 78-88; Engl. transl.: J. Soviet Math. 52 (1990), no. 5, 3403-3410.

Regularizability of operators, inverse to linear injections and to superposition of them (Russian), Sibirsk. Mat. Zh. 29 (1988), no. 3, 190-193; Engl. transl.: Siberian Math. J. 29

(1988), no. 3, 488-491 (with E. N. Domanskii).

The Banach-Saks and Mazur properties in Banach spaces (Russian), Mat. Zametki 42 (1987), no. 6, 786-789; Engl. transl.: Math. Notes 42 (1987), no. 5-6, 931-933.

Banach-Saks properties and the three space problem (Russian), in: “Operators in function spaces and problems in function theory” (ed.by V. A. Marchenko), Kiev, Naukova Dumka, 1987, p. 96-105 (with A.Plichko).

w*-derivatives of transfinite order of the subspaces of a conjugate Banach space (Russian, Ukrainian, English summary), Dokl. Akad. Nauk Ukrain. SSR. Ser. A, 1987, no. 10, 9-12.

A comparison between the weak and the continuous Banach-Saks properties (Russian), Teor. Funktsii, Funktsion. Anal. i Prilozhen. 48 (1987), 130-134; Engl. transl.: J. Soviet Math. 49 (1990), no. 2, 938-940.

Properties of Banach spaces stable and unstable with respect to the gap (Russian), Sibirsk. Mat. Zh. 28 (1987), no. 1, 182-184; Engl. transl.: Siberian Math. J., 28 (1987), no. 1, 140-142.

Separably injective Banach spaces (Russian), Funktsional. Anal. i Prilozhen. 20 (1986), no. 2, 80-81; Engl. transl.: Functional Anal. Appl. 20 (1986), no. 2, 154-155.

Set of sums of conditionally convergent series in Banach spaces (Russian), Teor. Funktsii, Funktsion. Anal. i Prilozhen. 46 (1986), 77-85; Engl. transl.: J. Soviet Math. 48 (1990), no. 5, 559-566.

Diminishing of the spectrum of an operator under extension (Russian), Teor. Funktsii, Funktsion. Anal. i Prilozhen. 45 (1986), 96-97; Engl. transl.: J. Soviet Math, 48 (1990), no 4,

450-451.

The three space problem for the weak Banach-Saks property (Russian), Mat. Zametki 38 (1985), no. 5, 721-725; Engl. transl.: Math. Notes 38 (1985), no. 5-6, 905-907.

Banach-Saks properties in spaces with a symmetric basis (Russian, Ukrainian, English summary), Dokl. Akad. Nauk Ukrain. SSR, Ser. A, 1985, no. 8, 12-14.

Banach-Saks properties, injectivity and gaps between subspaces of a Banach space (Russian), Teor. Funktsii, Funktsion. Anal. i Prilozhen. 44 (1985), 69-78; Engl. transl.: J. Soviet Math. 48

(1990), no. 3, 299-306.

The relation of the gaps of subspaces to dimension and other isomorphic invariants (Russian, Armenian summary), Akad. Nauk Armyan. SSR Dokl. 79 (1984), no. 2, 51-53.

On the properties of the opening and related closeness characterizations of Banach spaces (Russian), Teor. Funktsii, Funktsion. Anal. i Prilozhen. 42 (1984), 97-107; Engl. transl.:

Amer. Math. Soc. Transl. (2), vol. 136 (1987), 109-119.

Functional Analysis

Graph Theory

Metric Geometry and Its Algorithmic Applications

Research Summary:

Analysis of large sets of data is important in many contexts. Usually data is endowed with a natural distance (degree of dissimilarity) of its elements. One of the useful approaches to analysis of such sets of data is to use some low-distortion embeddings of the set into a space whose structure is well-known, for example into a two-dimensional or three-dimensional space. After that one can use many algorithms available in computational geometry and many tools from such classical parts of mathematics as Calculus. In some cases one can even visualize the structure of the set, for example, see its clusters. Unfortunately the existence of a low-distortion embedding into a plane is rather rare in applications. In many contexts much weaker (than low-distortion) types of embeddings are still useful, and even embeddings into high-dimensional or infinite-dimensional generalizations of the three-dimensional space lead to important results. Constructions and analysis of such embeddings is the main goal of research of Dr. Mikhail Ostrovskii.