𝐶₁₁ contractions are reflexive

Wu, Pei Yuan

doi:10.1090/S0002-9939-1979-0539633-X

$C\sb{11}$ contractions are reflexive

Author: Pei Yuan Wu
Journal: Proc. Amer. Math. Soc. 77 (1979), 68-72
MSC: Primary 47A15
DOI: https://doi.org/10.1090/S0002-9939-1979-0539633-X
MathSciNet review: 539633
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that a completely nonunitary ${C_{11}}$ contraction defined on a separable Hilbert space with finite defect indices is reflexive.

[1] C. Apostol, Operators quasisimilar to a normal operator, Proc. Amer. Math. Soc. 53 (1975), 104-106. MR 0402522 (53:6341)
[2] N. Dunford and J. T. Schwartz, Linear operators, Part II, Interscience, New York, 1967.
[3] D. Sarason, Invariant subspaces and unstarred operator algebras, Pacific J. Math. 17 (1966), 511-517. MR 0192365 (33:590)
[4] B. Sz.-Nagy and C. Foias, Harmonic analysis of operators on Hilbert space, North-Holland, Amsterdam; Akadémiai Kiadó, Budapest, 1970. MR 0275190 (43:947)
[5] -, On the structure of intertwining operators, Acta Sci. Math. 35 (1973), 225-254. MR 0399896 (53:3737)
[6] P. Y. Wu, Bi-invariant subspaces of weak contractions, J. Operator Theory (to appear). MR 532877 (80k:47009)