Abstract
The Wielandt inequality asserts that if a positive operator A on a Hilbert space H satisfies 0 < m ≤ A ≤ M for some 0 < m < M, then
for every orthogonal pair x and y. In this paper, we show Wielandt type extensions of the Heinz-Kato-Furuta inequality, which is based on some generalizations of the Wielandt inequality by Fujii-Katayama-Nakamoto and Bauer-Householder. The obtained inequalities are simultaneous extensions of the Heinz-Kato-Furuta and the Wielandt inequalities. Related to our extensions, we discuss some applications of the Furuta inequality and the grand Furuta inequality.
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Fujii, M., Seo, Y. (2001). Wielandt type extensions of the Heinz—Kato—Furuta inequality. In: Kérchy, L., Gohberg, I., Foias, C.I., Langer, H. (eds) Recent Advances in Operator Theory and Related Topics. Operator Theory: Advances and Applications, vol 127. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8374-0_14
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DOI: https://doi.org/10.1007/978-3-0348-8374-0_14
Publisher Name: Birkhäuser, Basel
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