$C_{11}$ contractions are reflexive. II
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- by Pei Yuan Wu PDF
- Proc. Amer. Math. Soc. 82 (1981), 226-230 Request permission
Abstract:
It has been shown previously by the author that any completely nonunitary ${C_{11}}$ contraction with finite defect indices is reflexive. In this note we show that this is true even without the completely nonunitary assumption.References
- John B. Conway and Pei Yuan Wu, The splitting of $A(T_{1}\oplus T_{2})$ and related questions, Indiana Univ. Math. J. 26 (1977), no. 1, 41–56. MR 425673, DOI 10.1512/iumj.1977.26.26002
- James A. Deddens, Every isometry is reflexive, Proc. Amer. Math. Soc. 28 (1971), 509–512. MR 278099, DOI 10.1090/S0002-9939-1971-0278099-7
- James A. Deddens, Reflexive operators, Indiana Univ. Math. J. 20 (1971), no. 10, 887–889. MR 412847, DOI 10.1512/iumj.1971.20.20072
- Paul R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity, AMS Chelsea Publishing, Providence, RI, 1998. Reprint of the second (1957) edition. MR 1653399
- 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
- D. Sarason, Invariant subspaces and unstarred operator algebras, Pacific J. Math. 17 (1966), 511–517. MR 192365, DOI 10.2140/pjm.1966.17.511
- 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
- John Wermer, On invariant subspaces of normal operators, Proc. Amer. Math. Soc. 3 (1952), 270–277. MR 48700, DOI 10.1090/S0002-9939-1952-0048700-X
- Pei Yuan Wu, $C_{11}$ contractions are reflexive, Proc. Amer. Math. Soc. 77 (1979), no. 1, 68–72. MR 539633, DOI 10.1090/S0002-9939-1979-0539633-X
- Pei Yuan Wu, On a conjecture of Sz.-Nagy and Foiaş, Acta Sci. Math. (Szeged) 42 (1980), no. 3-4, 331–338. MR 603322
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 226-230
- MSC: Primary 47A15; Secondary 47A45, 47C05
- DOI: https://doi.org/10.1090/S0002-9939-1981-0609656-X
- MathSciNet review: 609656