Unitary asymptotes of Hilbert space operators

Kérchy, László

Banach Center Publications, Tome 29 (1994), p. 191-201 / Harvested from The Polish Digital Mathematics Library

Résumé

In this survey article we are going to present the effectiveness of the use of unitary asymptotes in the study of Hilbert space operators.

Détail

Publié le : 1994-01-01

Zbl 0807.47005

EUDML-ID : urn:eudml:doc:262850

Bibliographie

[000] [1] S. Banach, Théorie des Opérations Linéaires, Chelsea, New York, 1955. | Zbl 0067.08902

[001] [2] H. Bercovici, Operator Theory and Arithmetic in $H^∞$, Math. Surveys Monographs 26, Amer. Math. Soc., Providence, R.I., 1988.

[002] [3] H. Bercovici, Commuting power-bounded operators, Acta Sci. Math. (Szeged) 57 (1993), 55-64. | Zbl 0819.47017

[003] [4] H. Bercovici and L. Kérchy, On the spectra of $C_{11}$-contractions, Proc. Amer. Math. Soc. 95 (1985), 412-418. | Zbl 0606.47014

[004] [5] H. Bercovici and K. Takahashi, On the reflexivity of contractions on Hilbert space, J. London Math. Soc. (2) 32 (1985), 149-156. | Zbl 0536.47009

[005] [6] J. B. Conway, A Course in Functional Analysis, Springer, New York, 1985. | Zbl 0558.46001

[006] [7] M. Day, Means for bounded functions and ergodicity of the bounded representations of semigroups, Trans. Amer. Math. Soc. 69 (1950), 276-291. | Zbl 0039.12301

[007] [8] J. A. Deddens and P. A. Fillmore, Reflexive linear transformations, Linear Algebra Appl. 10 (1975), 89-93. | Zbl 0301.15011

[008] [9] N. Dunford and J. Schwartz, Linear Operators. II, Interscience, New York, 1963.

[009] [10] S. R. Foguel, A counterexample to a problem of Sz.-Nagy, Proc. Amer. Math. Soc. 15 (1964), 788-790. | Zbl 0124.06602

[010] [11] P. R. Halmos, On Foguel's answer to Nagy's question, ibid., 791-793. | Zbl 0123.09701

[011] [12] H. Helson, Lectures on Invariant Subspaces, Academic Press, New York, 1964.

[012] [13] E. Hewitt and K. Ross, Abstract Harmonic Analysis. I, Springer, Berlin, 1963. | Zbl 0115.10603

[013] [14] E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc., Providence, 1957.

[014] [15] T. B. Hoover, Quasi-similarity of operators, Illinois J. Math. 16 (1972), 678-686. | Zbl 0249.47014

[015] [16] L. Kérchy, A description of invariant subspaces of $C_{11}$-contractions, J. Operator Theory 15 (1986), 327-344. | Zbl 0602.47004

[016] [17] L. Kérchy, Contractions being weakly similar to unitaries, in: Oper. Theory: Adv. Appl. 17, Birkhäuser, Basel, 1986, 187-200. | Zbl 0586.47008

[017] [18] L. Kérchy, On the spectra of contractions belonging to special classes, J. Funct. Anal. 67 (1986), 153-166. | Zbl 0588.47014

[018] [19] L. Kérchy, On the residual parts of completely non-unitary contractions, Acta Math. Hungar. 50 (1987), 127-145. | Zbl 0632.47006

[019] [20] L. Kérchy, Invariant subspaces of $C_{1·}$-contractions with non-reductive unitary extensions, Bull. London Math. Soc. 19 (1987), 161-166. | Zbl 0594.47007

[020] [21] L. Kérchy, On a conjecture of Teodorescu and Vasyunin, in: Oper. Theory: Adv. Appl. 28, Birkhäuser, Basel, 1988, 169-172. | Zbl 0649.47004

[021] [22] L. Kérchy, Isometric asymptotes of power bounded operators, Indiana Univ. Math. J. 38 (1989), 173-188. | Zbl 0693.47014

[022] [23] L. Kérchy, On the functional calculus of contractions with nonvanishing unitary asymptotes, Michigan Math. J. 37 (1990), 323-338. | Zbl 0744.47011

[023] [24] L. Kérchy, On the reducing essential spectra of contractions, Acta Sci. Math. (Szeged) 57 (1993), 175-198. | Zbl 0818.47006

[024] [25] N. K. Nikolskiĭ and V. I. Vasyunin, A unified approach to function models, and the transcription problem, in: Oper. Theory: Adv. Appl. 41, Birkhäuser, Basel, 1989, 405-434. | Zbl 0685.47006

[025] [26] V. V. Peller, Estimates of functions of power bounded operators on Hilbert space, J. Operator Theory 7 (1982), 341-372. | Zbl 0485.47007

[026] [27] V. Pták, Construction of dilations, Exposition. Math. 10 (1992), 151-170. | Zbl 0778.47007

[027] [28] H. Radjavi and P. Rosenthal, Invariant Subspaces, Springer, New York, 1973. | Zbl 0269.47003

[028] [29] F. Riesz and B. Sz.-Nagy, Functional Analysis, Ungar, New York, 1955.

[029] [30] W. Rudin, Functional Analysis, McGraw-Hill, New York, 1973.

[030] [31] N. Salinas, Reducing essential eigenvalues, Duke Math. J. 40 (1973), 561-580. | Zbl 0292.47001

[031] [32] D. Sarason, Invariant subspaces and unstarred operator algebras, Pacific J. Math. 17 (1966), 511-517. | Zbl 0171.33703

[032] [33] B. Sz.-Nagy, On uniformly bounded linear transformations in Hilbert space, Acta Sci. Math. (Szeged) 11 (1947), 152-157.

[033] [34] B. Sz.-Nagy, Sur les contractions de l'espace de Hilbert, ibid. 15 (1953), 87-92. | Zbl 0052.12203

[034] [35] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland and Akadémiai Kiadó, Amsterdam-Budapest, 1970.

[035] [36] K. Takahashi, The reflexivity of contractions with nonreductive *-residual parts, Michigan Math. J. 34 (1987), 153-159. | Zbl 0618.47011

[036] [37] W. R. Wogen, On reflexivity and quasisimilarity, preprint.