Seminormality of operators from their tensor product. (English) Zbl 0855.47018

Summary: The question of seminormality of tensor products of nonzero bounded linear operators on Hilbert spaces is investigated. It is shown that \(A\otimes B\) is subnormal if and only if so are \(A\) and \(B\).


47B20 Subnormal operators, hyponormal operators, etc.
47A80 Tensor products of linear operators
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[1] Christian Berg, Jens Peter Reus Christensen, and Paul Ressel, Harmonic analysis on semigroups, Graduate Texts in Mathematics, vol. 100, Springer-Verlag, New York, 1984. Theory of positive definite and related functions. · Zbl 0619.43001
[2] Kevin Clancey, Seminormal operators, Lecture Notes in Mathematics, vol. 742, Springer, Berlin, 1979. · Zbl 0435.47032
[3] John B. Conway, The theory of subnormal operators, Mathematical Surveys and Monographs, vol. 36, American Mathematical Society, Providence, RI, 1991. · Zbl 0743.47012
[4] R. Gellar and L. J. Wallen, Subnormal weighted shifts and the Halmos-Bram criterion, Proc. Japan Acad. 46 (1970), 375 – 378. · Zbl 0217.45501
[5] P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887 – 933. · Zbl 0204.15001
[6] Alan Lambert, Subnormality and weighted shifts, J. London Math. Soc. (2) 14 (1976), no. 3, 476 – 480. · Zbl 0358.47014
[7] Mircea Martin and Mihai Putinar, Lectures on hyponormal operators, Operator Theory: Advances and Applications, vol. 39, Birkhäuser Verlag, Basel, 1989. · Zbl 0684.47018
[8] Allen L. Shields, Weighted shift operators and analytic function theory, Topics in operator theory, Amer. Math. Soc., Providence, R.I., 1974, pp. 49 – 128. Math. Surveys, No. 13. · Zbl 0303.47021
[9] J. A. Shohat and J. D. Tamarkin, The problem of moments, Amer. Math. Soc., Providence, RI, 1943. · Zbl 0063.06973
[10] J. Stochel and F. H. Szafraniec, On normal extensions of unbounded operators. II, Acta Sci. Math. (Szeged) 53 (1989), no. 1-2, 153 – 177. · Zbl 0698.47003
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