Tagged Questions
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1answer
52 views
exercise: limit orthonormal sequence, “Banach Space Theory”
I have an exercise from "Banach Space Theory":
Suppose $\{x^k\}_{k=1}^\infty$ is an orthonormal sequence in $l_2$, where $x^k:=(x_i^k)$. Show that $\lim_{k\rightarrow \infty} x_i^k =0 \ \forall_{i\in ...
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0answers
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Maximal ideals in the algebra of continuously differentiable functions on [0,1]
This is an exercise in Rudin's Functional Analysis, in the chapter on commutative Banach algebras. My (uneducated) guess was that every homomorphism on $C^{1}[0,1]$ is an evaluation at some point of ...
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0answers
34 views
Unbounded self- adjoint and von Neumann algebra
I am reading Conway's Functional Analysis. Here is one exercise problem.I don't know how to show the following fact. For unbounded self-adjoint $T$ in Hilbert space $H$
1) $T$ commutes with its Borel ...
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1answer
39 views
Weak convergence-exercice
Let $\Omega$ be an open set in $\mathbb{R}^n$ and let $(u_n)$ be a bounded sequence in $H^1_0(\Omega).$
Who's the theorem say that we can extract a subsequence denoted $u_{n}$ as $u_n$ weakly ...
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2answers
115 views
$C^\infty(R^n)$ is a Banach Space when equipped with topology of uniform convergence
Prove $C^\infty(\Bbb R^n)$ is a Banach Space when equipped with topology of uniform convergence.
$C^\infty(\Bbb R^n)$ is space of all continuous functions that converge to $0$ at $\infty$.
And, the ...
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2answers
264 views
problem books in functional analysis
There are many excellent problem books in real analysis.I'm looking for a problem book in functional analysis or a book which contains a lot of problems in functional analysis (Easy and hard problems) ...
2
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1answer
201 views
Hellinger-Toeplitz theorem use principle of uniform boundedness
Suppose $T$ is an everywhere defined linear map from a Hilbert space $\mathcal{H}$ to itself. Suppose $T$ is also symmetric so that $\langle Tx,y\rangle=\langle x,Ty\rangle$ for all ...
