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A NOTE ON k-HYPERREFLEXIVITY OF TOEPLITZ-HARMONIC SUBSPACES

Budzynski, Piotr;Piwowarczyk, Kamila;Ptak, Marek

  • 투고 : 2013.11.08
  • 발행 : 2014.11.30

초록

The 2-hyperreflexivity of Toeplitz-harmonic type subspace generated by an isometry or a quasinormal operator is shown. The k-hyperreflexivity of the tensor product $\mathcal{S}{\otimes}\mathcal{V}$ of a k-hyperreflexive decom-posable subspace $\mathcal{S}$ and an abelian von Neumann algebra $\mathcal{V}$ is established.

키워드

k-hyperreflexive subspace;direct integral;tensor product;isometry;quasinormal operator

참고문헌

  1. K. R. Davidson, The distance to the analytic Toeplits operators, Illinois J. Math. 7 (1987), no. 2, 265-273.
  2. E. Azoff and M. Ptak, A dichotomy for linear spaces of Toeplitz Operators, J. Funct. Anal. 156 (1998), no. 2, 411-428. https://doi.org/10.1006/jfan.1998.3275
  3. A. Brown, On a class of operators, Proc. Amer. Math. Soc. 4 (1953), 723-728. https://doi.org/10.1090/S0002-9939-1953-0059483-2
  4. J. B. Conway, A Course in Operator Theory, American Mathematical Society, Providence, RI, 2000.
  5. J. B. Conway and M. Ptak, The harmonic functional calculus and hyperreflexivity, Pacific J. Math. 204 (2002), no. 1, 19-29. https://doi.org/10.2140/pjm.2002.204.19
  6. J. Dixmier, Von Neumann Algebras, North-Holland, Amsterdam, 1981.
  7. D. Hadwin and E. A. Nordgren, Subalgebras of reflexive algebras, J. Operator Theory 7 (1982), no. 1, 3-23.
  8. D. Hadwin and E. A. Nordgren, Erratum-subalgebras of reflexive algebras, J. Operator Theory 15 (1986), no. 1, 203-204.
  9. D. Hadwin, A general view of reflexivity, Trans. Amer. Math. Soc. 344 (1994), no. 1, 325-360. https://doi.org/10.1090/S0002-9947-1994-1239639-4
  10. K. Klis and M. Ptak, Quasinormal operators and reflexive subspaces, Rocky Mountain J. Math. 33 (2003), no. 4, 1395-1402. https://doi.org/10.1216/rmjm/1181075470
  11. K. Klis and M. Ptak, Quasinormal operators are hyperreflexive, Topological algebras, their applications, and related topics, 241-244, Banach Center Publ., 67, Polish Acad. Sci., Warsaw, 2005.
  12. K. Klis and M. Ptak, k-hyperreflexive subspaces, Houston J. Math. 32 (2006), no. 1, 299-313.
  13. J. Kraus and D. Larson, Reflexivity and distance formulae, Proc. London Math. Soc. 53 (1986), no. 2, 340-356.
  14. M. Ptak, Projections onto the spaces of Toeplitz operators, Ann. Polon. Math. 86 (2005), no. 2, 97-105. https://doi.org/10.4064/ap86-2-1
  15. S. Rosenoer, Distance estimates for von Neumann algebras, Proc. Amer. Math. Soc. 86 (1982), no. 2, 248-252. https://doi.org/10.1090/S0002-9939-1982-0667283-3
  16. S. Rosenoer, Nehari's theorem and the tensor product of hyper-reflexive algebras, J. London Math. Soc. 47 (1993), no. 2, 349-357.
  17. J. T. Schwartz, $W^*$-Algebras, Gordon and Breach, New York, 1967.

과제정보

연구 과제 주관 기관 : NCN (National Science Center)