Abstract
J. Arhippainen and V. Müller showed that $\|a + \lambda e\|_1 \leq 3\|a + \lambda e\|_{\operatorname{op}}$ for all $a + \lambda e \in \tilde{A}$, where $\tilde{A}$ is the unitization of an arbitrary non-unital Banach algebra $A$ with regular norm. In this note, we present a necessary and sufficient condition for the equality of this estimate and its related problem.
Citation
Sin-Ei Takahasi. Takeshi Miura. Takahiro Hayata. "An Equality Condition of Arhippainen-Müller's Estimate and its Related Problem." Taiwanese J. Math. 15 (1) 165 - 169, 2011. https://doi.org/10.11650/twjm/1500406167
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