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Abstrakty
Power partial isometries are not always hyperreflexive neither reflexive. In the present paper it will be shown that power partial isometries are always hyporeflexive and 2-hyperreflexive.
Czasopismo
Rocznik
Tom
Strony
799–--806
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- Department of Applied Mathematics University of Agriculture ul. Balicka 253c, 30-198 Kraków, Poland
autor
- Department of Applied Mathematics University of Agriculture ul. Balicka 253c, 30-198 Kraków, Poland
Bibliografia
- [1] W.T. Arveson, Interpolation problems in nest algebras, J. Funct. Anal. 20, (1975), 208-233.
- [2] W.T. Arveson, Ten lectures on operator algebras, CBMS Regional Conference Series 55, Amer. Math. Soc, Providence (1984).
- [3] E.A. Azoff, k-reflexivity in finite dimensional subspaces, Duke Math. J. 40 (1973), 821-830.
- [4] E.A. Azoff, CK. Fong, F. Gilfeather, A reduction theory for non-self-adjoint operator-algebras, Trans. Amer. Math. Soc. 224 (1976), 351-366.
- [5] E.A. Azoff, W.S. Li, M. Mbekhta, M. Ptak, On consistent operators and reflexivity, Integr. Equ. Oper. Theory 71 (2011), 1-12.
- [6] H. Bercovici, Operator theory and arytmetic in H°°, Mathematical Surveys and Monographs, vol. 26, Amer. Math. Soc, 1988.
- [7] H. Bercovici, C. Foias, C. Pearcy, Dual Algebras with Applications to Invariant Sub-spaces and Dilation Theory, CBMS Regional Conference Series 56, Amer. Math. Soc, Providence, 1985.
- [8] L. Brickman, P.A. Fillmore, The invariant subspace lattice of a linear transformation, Canad. J. Math. 19 (1967), 810-822.
- [9] J.B. Conway, A Course in Operator Theory, Amer. Math. Soc, Providence, 2000.
- [10] K.R. Davidson, The distance to the analytic Toeplitz operators, Illinois J. Math. 31 (1987), 265-273.
- [11] J.A. Deddens, P.A. Fillmore, Reflexive linear transformations, Linear Algebra Appl. 10 (1975), 89-93.
- [12] D. Hadwin, A general view of reflexivity, Trans. Amer. Math. Soc. 344 (1994), 325-360.
- [13] D. Hadwin, E.A. Nordgren, Subalgebras of reflexive algebras, J. Operator Theory 7 (1982), 3-23.
- [14] P.R. Halmos, L.J. Wallen, Powers of Partial Isometries, J. Math. Mech. 19 (1970), 657-663.
- [15] K. Kliś, M. Ptak, Quasinormal operators are hyperreflexive, Banach Center Publ. 67 (2005), 241-244.
- [16] K. Kliś, M. Ptak, k-hyperreflexive subspaces, Houston J. Math. 32 (2006), 299-313.
- [17] J. Kraus, D.R. Larson, Reflexivity and distance formulae, Proc. Lond. Math. Soc. 53 (1986), 340-356.
- [18] A.I. Loginov, V.I. Shulman, Hereditary and intermediate reflexivity of W* algebras, Math. USSR-Izv. 9 (1975), 1189-1201.
- [19] W.E. Longstaff, On the operation Alg Lat in finite dimensions, Linear Algebra Appl. 27 (1979), 27-29.
- [20] V. Muller, M. Ptak, Hyperreflexivity of finite-dimensional sub space, J. Funct. Anal. 218 (2005), 395-408.
- [21] K. Piwowarczyk, M. Ptak, On the hyperreflexivity of power partial isometries, Linear Algebra Appl. 437 (2012), 623-629.
- [22] H. Radjavi, P. Rosenthal, Invariant Subspaces, Springer-Verlag, Berlin-Heidberg-New York, 1973.
- [23] S. Rosenoer, Distance estimates for von Neumann algebras, Proc. Amer. Math. Soc. 86 (1982) 2, 248-252.
- [24] D. Sarason, Invariant subspaces and unstarred operator algebras, Pacific J. Math. 17 (1966), 511-517.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6c4d9e6f-b8d2-4a10-a9c0-81fadd935d44
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