The operator inequality $P\leq A^ *PA$
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- by B. P. Duggal PDF
- Proc. Amer. Math. Soc. 109 (1990), 697-698 Request permission
Abstract:
A short proof of the result that if $P$ is a positive compact operator and $A$ is a contraction such that $p \leq {A^*}PA$, then $P = {A^*}PA,\overline {\operatorname {ran} } P$ reduces $A$ and $A|\overline {\operatorname {ran} } P$ is unitary is given.References
- R. G. Douglas, On the operator equation $S^{\ast } XT=X$ and related topics, Acta Sci. Math. (Szeged) 30 (1969), 19–32. MR 250106
- B. P. Duggal, On intertwining operators, Monatsh. Math. 106 (1988), no. 2, 139–148. MR 968331, DOI 10.1007/BF01298834
- Paul Richard Halmos, A Hilbert space problem book, 2nd ed., Encyclopedia of Mathematics and its Applications, vol. 17, Springer-Verlag, New York-Berlin, 1982. MR 675952, DOI 10.1007/978-1-4684-9330-6
- M. Radjabalipour, An extension of Putnam-Fuglede theorem for hyponormal operators, Math. Z. 194 (1987), no. 1, 117–120. MR 871223, DOI 10.1007/BF01168010
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 697-698
- MSC: Primary 47B15; Secondary 47A62, 47B20
- DOI: https://doi.org/10.1090/S0002-9939-1990-1007495-7
- MathSciNet review: 1007495