On polynomially bounded operators with rich spectrum

Gadidov, Radu

doi:10.1090/S0002-9939-1995-1243168-8

On polynomially bounded operators with rich spectrum
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by Radu Gadidov

Proc. Amer. Math. Soc. 123 (1995), 2133-2139

DOI: https://doi.org/10.1090/S0002-9939-1995-1243168-8

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Abstract:

D. Westood (J. Funct. Anal. 66 (1986), 96-104) proved that ${C_{00}}$-contractions with dominating spectrum are in ${\mathbb {A}_{{\aleph _0}}}$. We generalize this result to polynomially bounded operators.

References

Hari Bercovici, A contribution to the structure theory of operators in the class $\textbf {A}$, J. Funct. Anal. 78 (1988), no. 2, 197–207. MR 943497, DOI 10.1016/0022-1236(88)90118-8
Hari Bercovici, Ciprian Foias, and Carl Pearcy, Dual algebras with applications to invariant subspaces and dilation theory, CBMS Regional Conference Series in Mathematics, vol. 56, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1985. MR 787041, DOI 10.1090/cbms/056
H. Bercovici, C. Foiaş, C. M. Pearcy, and B. Sz.-Nagy, Functional models and extended spectral dominance, Acta Sci. Math. (Szeged) 43 (1981), no. 3-4, 243–254. MR 640300
H. Bercovici, C. Foias, and C. Pearcy, Two Banach space methods and dual operator algebras, J. Funct. Anal. 78 (1988), no. 2, 306–345. MR 943501, DOI 10.1016/0022-1236(88)90122-X
Scott Brown and Bernard Chevreau, Toute contraction à calcul fonctionnel isométrique est réflexive, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), no. 5, 185–188 (French, with English summary). MR 955549
Bernard Chevreau and Carl Pearcy, On the structure of contraction operators. I, J. Funct. Anal. 76 (1988), no. 1, 1–29. MR 923042, DOI 10.1016/0022-1236(88)90046-8
Bernard Chevreau, George Exner, and Carl Pearcy, On the structure of contraction operators. III, Michigan Math. J. 36 (1989), no. 1, 29–62. MR 989936, DOI 10.1307/mmj/1029003881
B. Chevreau, C. M. Pearcy, and A. L. Shields, Finitely connected domains $G$, representations of $H^{\infty }(G)$, and invariant subspaces, J. Operator Theory 6 (1981), no. 2, 375–405. MR 643698
Jacques Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (Algèbres de von Neumann), Cahiers Scientifiques, Fasc. XXV, Gauthier-Villars, Paris, 1957 (French). MR 0094722

Representations of

and invariant subspaces

On polynomially bounded operators

Wing Suet Li, On polynomially bounded operators. I, Houston J. Math. 18 (1992), no. 1, 73–96. MR 1159441

On polynomially bounded operators

Béla Sz.-Nagy and Ciprian Foiaş, Harmonic analysis of operators on Hilbert space, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest, 1970. Translated from the French and revised. MR 0275190
Vern Paulsen, Carl Pearcy, and Srdjan Petrović, On centered and weakly centered operators, J. Funct. Anal. 128 (1995), no. 1, 87–101. MR 1317711, DOI 10.1006/jfan.1995.1024

On

contractions with dominating spectrum

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