Quasi-similarity of weak contractions
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- by Pei Yuan Wu PDF
- Proc. Amer. Math. Soc. 69 (1978), 277-282 Request permission
Abstract:
Let T be a completely nonunitary (c.n.u.) weak contraction (in the sense of Sz.-Nagy and Foiaş). We show that T is quasi-similar to the direct sum of its ${C_0}$ part and ${C_{11}}$ part. As a corollary, two c.n.u. weak contractions are quasi-similar to each other if and only if their ${C_0}$ parts and ${C_{11}}$ parts are quasi-similar to each other, respectively. We also completely determine when c.n.u. weak contractions and ${C_0}$ contractions are quasi-similar to normal operators.References
- Constantin Apostol, Operators quasisimilar to a normal operator, Proc. Amer. Math. Soc. 53 (1975), no. 1, 104–106. MR 402522, DOI 10.1090/S0002-9939-1975-0402522-1
- H. Bercovici, C. Foiaş, and B. Sz.-Nagy, Compléments à l’étude des opérateurs de classe $C_{O}$. III, Acta Sci. Math. (Szeged) 37 (1975), no. 3-4, 313–322 (French). MR 394251
- Ion Colojoară and Ciprian Foiaş, Theory of generalized spectral operators, Mathematics and its Applications, Vol. 9, Gordon and Breach Science Publishers, New York-London-Paris, 1968. MR 0394282
- 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
- R. G. Douglas, On the operator equation $S^{\ast } XT=X$ and related topics, Acta Sci. Math. (Szeged) 30 (1969), 19–32. MR 250106
- Ali A. Jafarian, Weak contractions of Sz.-Nagy and Foiaş are decomposable, Rev. Roumaine Math. Pures Appl. 22 (1977), no. 4, 489–497. MR 448149
- T. L. Kriete III, Similarity of canonical models, Bull. Amer. Math. Soc. 76 (1970), 326–330. MR 254650, DOI 10.1090/S0002-9904-1970-12462-4
- C. R. Putnam, An inequality for the area of hyponormal spectra, Math. Z. 116 (1970), 323–330. MR 270193, DOI 10.1007/BF01111839
- 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
- Pei Yuan Wu, On nonorthogonal decompositions of certain contractions, Acta Sci. Math. (Szeged) 37 (1975), no. 3-4, 301–306. MR 399897
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 69 (1978), 277-282
- MSC: Primary 47A45
- DOI: https://doi.org/10.1090/S0002-9939-1978-0482302-4
- MathSciNet review: 0482302