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For a hermitian element $a$ in a $C^*$-algebra, show that $\|a^{2n}\| = \|a\|^{2n}$

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#functional-analysis #c-star-algebras #banach-algebras
36
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Diffeomorphism in Banach algebra

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#analysis #banach-algebras
111
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Semi-direct decompositions of Banach algebras

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#banach-algebras #direct-sum #algebras
88
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isometrically isomorphism

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#general-topology #banach-spaces #banach-algebras
729
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Compact operators and essential spectral radius

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#functional-analysis #spectral-theory #banach-algebras
427
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Understanding a proof from Conway: showing existence of idempotents using functional calculus

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#functional-analysis #spectral-theory #banach-algebras
439
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For a Banach algebra $\mathcal{A}$ and an idempotent $e$, show that $\mathcal{A}e$ is a Banach algebra

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#functional-analysis #spectral-theory #banach-algebras
6.8k
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Proof of Gelfand formula for spectral radius

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#functional-analysis #spectral-theory #banach-algebras
45
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Is this true? If ‎$‎\varphi\in ‎\mathcal{B}(E,F)‎$‎ and preserving density, then $‎\varphi‎$‎ is surjection. Why?

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#banach-algebras
69
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Is this true? If ‎$‎\varphi\in ‎\mathcal{B}_{‎\mathcal{A}}(E,F)‎$‎ and preserving density, then $‎\varphi‎$‎ is surjection

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#banach-algebras
254
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Maximal ideal space

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#functional-analysis #operator-theory #c-star-algebras #banach-algebras
34
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Let $A=\mathbb{C}$ and $E=F=C[0,1]$. Are $E=F$ Hilbert $\mathbb{C}^*$-modules?

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#banach-algebras
69
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Specific question on Banach space over nonarchimedean field

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#functional-analysis #reference-request #banach-spaces #banach-algebras
1k
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A question about locally compact Hausdorff space

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#general-topology #functional-analysis #banach-algebras
58
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Banach algebra of homomorphisms

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#banach-spaces #banach-algebras

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