List questions from banach-algebras

Published on 27 Mar 2026 - 5:34

92

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For any two positive operator $a,b$ with norm $<1$ there is a $c$ such that $a,b\leq c$ and $\|c\|<1$. Does this hold for $\|a\|=\|b\|=1$?

Published on 22 Jul 2020 - 23:30

467

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What is the maximal ideal space of $H^\infty$?

Published on 09 Jul 2016 - 13:50

215

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If B(X) is isomorphic to B(Y), does that mean X is isomorphic to Y (for X and Y Banach spaces)?

Published on 09 Jul 2016 - 22:50

247

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Uses of spectral radius equal to norm.

Published on 26 Mar 2026 - 12:46

587

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Is the range of the Gelfand transform closed?

Published on 23 Feb 2026 - 1:04

158

Views

Spectral radius of an invertible element in a Banach algebra.

Published on 26 Mar 2026 - 12:48

120

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Why are two characters of a commutative Banach algebra with the same kernel equal?

Published on 12 Jul 2016 - 21:44

941

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Correspondence between maximal ideals and multiplicative functionals of a non unital, commutative Banach algebra.

Published on 12 Jul 2016 - 22:47

119

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About the Banach algebra $\ell^{\infty} (K( \ell^{1}))$

Published on 27 Mar 2026 - 13:27

116

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R.Douglas "Banach Algebra Technique Operator Theory" - Chapter 2 issue

Published on 19 Jul 2016 - 23:28

61

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Show that the Gelfand transform is a morphism?

Published on 20 Jul 2016 - 19:16

308

Views

Commutative Banach algebra and its maximal ideal space

Published on 21 Jul 2016 - 23:32

188

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Commutative Banach algebra and its Gelfand spectrum

Published on 22 Jul 2016 - 2:02

113

Views

Algebra $A$ and its Gelfand spectrum

Published on 22 Jul 2016 - 9:57

List Question

Is $\mathcal{L}(V)^*$ path connected?

For any two positive operator $a,b$ with norm $<1$ there is a $c$ such that $a,b\leq c$ and $\|c\|<1$. Does this hold for $\|a\|=\|b\|=1$?

What is the maximal ideal space of $H^\infty$?

If B(X) is isomorphic to B(Y), does that mean X is isomorphic to Y (for X and Y Banach spaces)?

Uses of spectral radius equal to norm.

Is the range of the Gelfand transform closed?

Spectral radius of an invertible element in a Banach algebra.

Why are two characters of a commutative Banach algebra with the same kernel equal?

Correspondence between maximal ideals and multiplicative functionals of a non unital, commutative Banach algebra.

About the Banach algebra $\ell^{\infty} (K( \ell^{1}))$

R.Douglas "Banach Algebra Technique Operator Theory" - Chapter 2 issue

Show that the Gelfand transform is a morphism?

Commutative Banach algebra and its maximal ideal space

Commutative Banach algebra and its Gelfand spectrum

Algebra $A$ and its Gelfand spectrum

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