Results 111 to 112 of about 127 (112)

Parametrized Furuta Inequality and its Application

2001
As generalizations of the Furuta inequality and grand Furuta inequality, we give parametrized forms of them; if A ≥ B > 0, then $$ {A^u}{\sharp _{\frac{{\delta - u}}{{p - u}}}}{B^{p \leqslant }}{B^\delta } $$ for u ≤ 0, 0 ≤ δ ≤ p and $$ {A^u}{\sharp _{\frac{{\delta - u}}{{\beta - u}}}}\left( {{A^t}{\natural _{\frac{{\beta - t}}{{p - t}}}}{B ...
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Chaotic order and Furuta inequality

2001
Summary: We show a satellite theorem of chaotic Furuta inequality. For positive invertible operators \(A\) and \(B\), if \(\log A\leq\log B\), then \[ (A^{{r\over 2}} B^p A^{{r\over 2}})^{{1+r\over p+r}}\leq A^{{r\over 2}} BA^{{r\over 2}}\quad\text{and}\quad (B^{{r\over 2}} A^p B^{{r\over 2}})^{{1+r\over p+r}}\geq B^{{r\over 2}} AB^{{r\over 2}} \] for \
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