On typical properties of Hilbert space operators
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- 作者：Tanja Eisner ; Tamás Mátrai
- 刊名：Israel Journal of Mathematics
- 出版年：2013
- 出版时间：June 2013
- 年：2013
- 卷：195
- 期：1
- 页码：247-281
- 全文大小：364KB
- 参考文献：1. S. A. Argyros and R. G. Haydon, / A hereditarily indecomposable L ?/sub>- / space that solves the scalar-plus-compact problem, Acta Mathematica <strong class="a-plus-plus">206strong> (2011), 1-4. CrossRef
2. S. Banach, / ”Uber die Baire’sche Kategorie gewisser Funktionenmengen, Studia Mathematica <strong class="a-plus-plus">3strong> (1931), 174-79.
3. W. Bartoszek and B. Kuna, / On residualities in the set of Markov operators on C 1, Proceedings of the American Mathematical Society <strong class="a-plus-plus">133strong> (2005), 2119-129. CrossRef
4. A. Bruckner, / Differentiation of Real Functions, Second edition, CRM Monograph Series, 5, American Mathematical Society, Providence, RI, 1994.
5. J. R. Choksi and M. G. Nadkarni, / Baire category in spaces of measures, unitary operators, and transformations, in / Proc. Int. Conference on Invariant Subspaces and Allied Topics, Narosa Publishers, New Delhi, 1986.
6. J. B. Conway, / A Course in Functional Analysis, Second edition, Graduate Texts in Mathematics 96, Springer-Verlag, New York, 1990.
7. G. Diestel and A. Koldobsky, / Sobolev spaces with only trivial isometries, Positivity <strong class="a-plus-plus">10strong> (2006), 135-44. CrossRef
8. T. Eisner, / Embedding operators into strongly continuous semigroups, Archiv der Mathematik <strong class="a-plus-plus">92strong> (2009), 451-60. CrossRef
9. T. Eisner, / A “typical-contraction is unitary, Enseignement des Mathématiques (2) <strong class="a-plus-plus">56strong> (2010), 403-10.
10. T. Eisner, / Stability of Operators and Operator Semigroups, Operator Theory: Advances and Applications, Vol. 209, Birkh?user Verlag, Basel, 2010.
11. T. Eisner, / Rigidity of contractions on Hilbert spaces, Groups, Geometry and Dynamics, to appear.
12. T. Eisner and A. Serény, / Category theorems for stable operators on Hilbert spaces, Acta Universitatis Szegediensis, Acta Scientiarum Mathematicarum <strong class="a-plus-plus">74strong> (2008), 259-70.
13. T. Eisner and A. Serény, / Category theorems for stable semigroups, Ergodic Theory and Dynamical Systems <strong class="a-plus-plus">29strong> (2009), 487-94. CrossRef
14. T. Eisner and A. Serény, / On the weak analogue of the Trotter-Kato theorem, Taiwanese Journal of Mathematics <strong class="a-plus-plus">14strong> (2010), 1411-416.
15. K.-J. Engel and R. Nagel, / One-parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, Vol. 194, Springer-Verlag, New York, 2000.
16. J. Feldman and R. V. Kadison, / The closure of the regular operators in a ring of operators, Proceedings of the American Mathematical Society <strong class="a-plus-plus">5strong> (1954), 909-16. CrossRef
17. V. Ferenczi and E. M. Galego, / Countable groups of isometries on Banach spaces, Transactions of the American Mathematical Society <strong class="a-plus-plus">362strong> (2010), 4385-431. CrossRef
18. P. R. Halmos, / In general a measure preserving transformation is mixing, Annals of Mathematics <strong class="a-plus-plus">45strong> (1944), 786-92. CrossRef
19. S. Jitomirskaya and B. Simon, / Operators with singular continuous spectrum. III. Almost periodic Schrdinger operators, Communications in Mathematical Physics <strong class="a-plus-plus">165strong> (1994), 201-05. CrossRef
20. A. S. Kechris, / Classical Descriptive Set Theory, Graduate Texts inMathematics, Vol. 156, Springer-Verlag, Berlin, 1994.
21. B. Kuna, / On residualities in the set of Markov continuous semigroups on C 1, Demonstratio Mathematica <strong class="a-plus-plus">39strong> (2006), 439-53.
22. J. Lamperti, / On the isometries of certain function-spaces, Pacific Journal of Mathematics <strong class="a-plus-plus">8strong> (1958) 459-66. CrossRef
23. S. Mazurkiewicz, / Sur les fonctions non dérivables, Studia Mathematica <strong class="a-plus-plus">3strong> (1931), 92-4.
24. M. G. Nadkarni, / Spectral Theory of Dynamical Systems, Birkh?user Advanced Texts: Basler Lehrbücher, Birkh?user Verlag, Basel, 1998. CrossRef
25. V. V. Peller, / Estimates of operator polynomials in the space L p / with respect to the multiplicative norm, Journal of Mathematical Sciences <strong class="a-plus-plus">16strong> (1981), 1139-149. CrossRef
26. W. C. Ridge, / Approximate point spectrum of a weighted shift, Transactions of the American Mathematical Society <strong class="a-plus-plus">147strong> (1970), 349-56. CrossRef
27. R. Del Rio, N. Makarov and B. Simon, / Operators with singular continuous spectrum. II. Rank one operators, Communications in Mathematical Physics <strong class="a-plus-plus">165strong> (1994), 59-7. CrossRef
28. V. A. Rohlin, / A “general-measure-preserving transformation is not mixing, Doklady Akad. Nauk SSSR <strong class="a-plus-plus">60strong> (1948), 349-51.
29. A. L. Shields, / Weighted shift operators and analytic function theory, in / Topics in Operator Theory, Math. Surveys, Vol. 13, American Mathematical Society, Providence, RI, 1974, pp. 49-28.
30. B. Simon, / Operators with singular continuous spectrum: I. General operators, Annals of Mathematics <strong class="a-plus-plus">141strong> (1995), 131-45. CrossRef
31. B. Sz?kefalvi-Nagy and C. Foia?, / Harmonic Analysis of Operators on Hilbert Space, North-Holland, Akadémiai Kiadó, Amsterdam, Budapest, 1970.
32. M. Takesaki, / Theory of Operator Algebras I, Springer-Verlag, New York-Heidelberg, 1979. CrossRef
33. Y.-C. Wong, / Introductory Theory of Topological Vector Spaces, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 167, Marcel Dekker, Inc., New York, 1992.
34. K. Yosida, / Functional Analysis, Sixth edition, Grundlehren der Mathematischen Wissenschaften, Vol. 123, Springer-Verlag, Berlin-New York, 1980. CrossRef
35. P. Zorin-Kranich, / Typical bounded operators admit common cyclic vectors, Proceedings of the American Mathematical Society, to appear. - 作者单位：Tanja Eisner (1)
Tamás Mátrai (2)
1. KdV Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE, Amsterdam, The Netherlands
2. Mathematics Department BA 6290, University of Toronto, 40 St. George St., M5S 2E4, Toronto, Ontario, Canada - ISSN：1565-8511
文摘
We study the typical behavior of bounded linear operators on infinite-dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral properties, the problem of unitary equivalence of typical operators, and their embeddability into C 0-semigroups. Our results provide information on the applicability of Baire category methods in the theory of Hilbert space operators.