Compact operators in the algebra generated by essentially unitary 𝐶₀ operators

Nordgren, Eric A.

doi:10.1090/S0002-9939-1975-0370222-2

Compact operators in the algebra generated by essentially unitary $C_{0}$ operators
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by Eric A. Nordgren PDF

Proc. Amer. Math. Soc. 51 (1975), 159-162 Request permission

Abstract:

It will be shown that the compact operators in the weakly closed algebra generated by an essentially unitary ${C_0}$ contraction are weakly dense in the algebra. The result implies the extension of a double dual theorem of Kriete, Moore and Page and yields a partial answer to a question on reductive algebras raised by Rosenthal.

References

P. Fatou, Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), no. 1, 335–400 (French). MR 1555035, DOI 10.1007/BF02418579
Ralph Gellar and Lavon Page, A new look at some familiar spaces of intertwining operators, Pacific J. Math. 47 (1973), 435–441. MR 328665, DOI 10.2140/pjm.1973.47.435
Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
T. L. Kriete III, Berrien Moore III, and Lavon B. Page, Compact intertwining operators, Michigan Math. J. 18 (1971), 115–119. MR 283591
Berrien Moore III and Eric Nordgren, On transitive algebras containing $C_{0}$ operators, Indiana Univ. Math. J. 24 (1974/75), 777–784. MR 361846, DOI 10.1512/iumj.1975.24.24062
Paul S. Muhly, Compact operators in the commutant of a contraction, J. Functional Analysis 8 (1971), 197–224. MR 0315486, DOI 10.1016/0022-1236(71)90010-3
Heydar Radjavi and Peter Rosenthal, Invariant subspaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 77, Springer-Verlag, New York-Heidelberg, 1973. MR 0367682, DOI 10.1007/978-3-642-65574-6
Peter Rosenthal, On commutants of reductive operator algebras, Duke Math. J. 41 (1974), 829–834. MR 358395

Analyse harmonique des opérateurs de l’espace de Hilbert

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