You are not currently logged in.
Access JSTOR through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Further Extension of the Heinz-Kato-Furuta Inequality
Proceedings of the American Mathematical Society
Vol. 127, No. 10 (Oct., 1999), pp. 2899-2904
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/119946
Page Count: 6
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
Let T be a bounded operator on a Hilbert space H, and A, B positive definite operators. Kato has shown that if |Tx|≤ |Ax| and |T*y|≤ |By| for all x, y ∈ H, then |(Tx,y)|≤ |f(A)x||g(B)y|, where f(t), g(t) are operator monotone functions defined on [0, ∞ ) such that f(t)g(t) = t. Furuta has shown that |(T|T|α +β -1x,y)|≤ |Aαx||Bβy|, where 0 ≤ α,β ≤ 1, 1 ≤ α +β . Let f(t), g(t) be any continuous operator monotone functions, and set h(t) = f(t)g(t)/t for t > 0. We will show that Th(|T|) is well defined and |(Th(|T|)x,y)|≤ |f(A)x||g(B)y|. Moreover, we will extend this result for unbounded closed operators densely defined on H.
Proceedings of the American Mathematical Society © 1999 American Mathematical Society