List questions from banach-algebras

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Prove a mapping $C(X,Y)\to \operatorname{Hom}(C(Y), C(X))$ is surjective

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The spectrum of a matrix operator is the set of its eigenvalues. But how to prove?

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Some concepts of $C^*$-algebra generalized from linear algebra. Can anyone help me to check if they are correct, and give some examples?

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To show an element in the sprectum of a matrix $M$ is negative in the spectrum of $-M$

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How can we use Hahn-Banach Theorem to prove a functional is linear and bounded?

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Prove that Banach algebra $B(X)$ has a unique (up to equivalence) complete algebra norm.

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Why is $E$ closed?

Published on 10 Apr 2026 - 21:29

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$GL_n^+(A)$ is open but $U_n^+(A)$ is not

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What is the limit of $\mathrm{Tr}(G^kM{G^*}^k)^{1/2k}$ when $k$ goes to infinity?

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Compute the norm of a bounded linear operator

Published on 08 Apr 2026 - 21:55

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Does Grothendieck's theorem hold for Bounded borel functions?

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Reference for Banach Lattices

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In Banach algebra $A$ if $a^2=a$ show that $\sigma_A(a)\subseteq\{0,1\}$

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Calculate $\operatorname{Rad}(A/\operatorname{Rad}(A))$ in a Banach algebra

Published on 14 Apr 2026 - 22:33

List Question

Exercise books in Banach algebra

Prove a mapping $C(X,Y)\to \operatorname{Hom}(C(Y), C(X))$ is surjective

The spectrum of a matrix operator is the set of its eigenvalues. But how to prove?

Some concepts of $C^*$-algebra generalized from linear algebra. Can anyone help me to check if they are correct, and give some examples?

To show an element in the sprectum of a matrix $M$ is negative in the spectrum of $-M$

How can we use Hahn-Banach Theorem to prove a functional is linear and bounded?

Prove that Banach algebra $B(X)$ has a unique (up to equivalence) complete algebra norm.

Why is $E$ closed?

$GL_n^+(A)$ is open but $U_n^+(A)$ is not

What is the limit of $\mathrm{Tr}(G^kM{G^*}^k)^{1/2k}$ when $k$ goes to infinity?

Compute the norm of a bounded linear operator

Does Grothendieck's theorem hold for Bounded borel functions?

Reference for Banach Lattices

In Banach algebra $A$ if $a^2=a$ show that $\sigma_A(a)\subseteq\{0,1\}$

Calculate $\operatorname{Rad}(A/\operatorname{Rad}(A))$ in a Banach algebra

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