All Questions
Tagged with fa.functional-analysis reference-request
1,021 questions
4
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Set of invertible operators in B(H) is connected. Is it true? Is there a reference?
Suppose $H$ is a Hilbert space, $B(H)$ is the algebra of bounded linear operators on it, $K(H)$ is ideal of compact operators in $B(H)$, $Inv(B(H)/K(H))$ is the topological group of invertible ...
- 11.1k
8
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1
answer
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Ring of continuous functions, reference request.
I am looking for a reference for the following facts in functional analysis and topology. (If these "facts" are not true, I suppose I'm looking for the closest approximation which is true.)
Let $X$ ...
- 13.3k
2
votes
2
answers
1k
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description of functions of conditionally negative type on a group
Recall that a kernel conditionaly of negative type on a set $X$ is a map $\psi:X\times X\rightarrow\mathbb{R}$ with the following properties:
1) $\psi(x,x)=0$
2) $\psi(y,x)=\psi(x,y)$
3) for any ...
- 11.1k
12
votes
1
answer
329
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Ideals in smooth subalgebras of C*-algebras
Let $B$ be a $C^{*}$-algebra and $\mathcal{B}$ a dense *-subalgebra stable under holomorphic functional calculus and $C^{1}$-functional calculus for selfadjoint elements. Also, $\mathcal{B}$ is a ...
- 25.8k
3
votes
0
answers
251
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What is the origin of the metrization problem for compact convex sets?
The following is an ``old question in analysis:''
Is it true that every perfectly normal compact convex subset of a locally convex topological vector space is metrizable?
Here perfectly normal means ...
- 3,547
4
votes
2
answers
580
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An analogue of Hilbert-Schmidt theorem for multilinear forms
Let $H$ be a (the) real separable Hilbert space. The Hilbert--Schmidt theorem says that a compact self-adjoint operator $A$ has an eigenfunction expansion. Instead of operator, we can think of a ...
- 1,612
3
votes
1
answer
181
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Reference request - spectral radius formula for linear transformations in char p
I am finishing up a paper and I would like to be able to quote a theorem that does what
is said in the title. To be specific let me introduce some notations:
${\bf F}$ is a local field of ...
- 3,702
3
votes
0
answers
223
views
Extension of positive operators and Bauer-Namioka
When $X$ is a vector subspace of an ordered vector space $A$, any positive linear functional $f: X \to R$ extends to all of $A$ as a positive linear functional provided one can find a nonvoid, ...
- 25.5k
0
votes
0
answers
301
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Lifting of product of a Banach algebra
Let $A$ be a non unital Banach algebra. The product induces a bounded linear map $T:A \otimes_{\gamma} A\to A$ where $\otimes_\gamma$ denotes the Banach projective tensor product.
A lifting of $T$ is ...
- 1,222
2
votes
1
answer
373
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Strong measurability reference
I'm reading a book on Lyapunov Exponents by Lian and Lu in which they refer to strong measurability of operator-valued maps. They define this by saying an operator valued map $T:\Omega\to L(X,X)$ is ...
- 41.1k
7
votes
1
answer
2k
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A good reference for the wave front set
Hello,
I am wondering whether anyone know some good references for the theory of wave front set, microlocal analysis? I have some basic knowledge of distribution theory at the level of the Rudin's ...
- 5,293
3
votes
1
answer
842
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An elementary introduction of Colombeau's generalized function theory
Hello, I am wondering whether anyone know an elementary reference for Colombeau's theory on the multiplication of distributions? I encountered the problem of the square of Delta function. I need a ...
- 5,984
9
votes
2
answers
2k
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Nice Classes of Non-Closable Operators
The only thing I know about non-closable operators can be summarised as "they exist, but they're nasty, so let's not talk about them!" This seems to be the case with everyone else I've talked to. I'd ...
- 511
7
votes
3
answers
4k
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infinitely many linear equations in infinitely many variables
Let $(a_{mn})_{m,n\in\mathbb{N}}$ and $(b_m)$ be sequences of complex numbers.We say that $(a_{mn})$ and $(b_m)$ constitute an infinite system of linear equations in infinitely many variables if we ...
7
votes
3
answers
1k
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Non-Borel subspace of Banach space
Let $X$ be a separable Banach space, $M \subset X$ a linear subspace. Must $M$ be a Borel set in $X$?
I believe the answer is "no," since I have seen authors who are careful to talk about "Borel ...
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6
votes
1
answer
453
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The typical size of a random element in a Banach space
Let $X$ be a separable Banach space, and let $\mathbb P$ be a Radon probability measure on $X$ with zero mean and covariance operator $K : X^* \to X$. Let $x$ be an $X$-valued random variable with ...
- 11.4k
8
votes
1
answer
920
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Looking for references talking about category of topological vector spaces
It's known that category of topological vector spaces is not abelian but quasi-abelian or exact category. I am looking for the references playing with this category(category theory). All the related ...
- 25.5k
1
vote
2
answers
3k
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unit sphere is weak dense in the unit ball
As I remember the following is true:
Fact: for every infinite-dimensional normed space $X$
the unit sphere $S$ is weak-dense in the unit ball $B$.
Please help me find a reference.
Thanks in ...
- 29.8k
11
votes
1
answer
654
views
Nonseparable Hilbert spaces as quotients of spaces of bounded functions
Is the following result true: the Hilbert space $\ell^{2}\left(2^{\Gamma}\right)$ is a quotient of $\ell^{\infty}\left(\Gamma\right)$ for any
uncountable $\Gamma$ ? [I think it is, but cannot remember ...
- 31.5k
6
votes
1
answer
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Reference needed for: every idempotent in a C*-algebra is similar to a hermitian one
The result stated in the title is thoroughly standard - or that's the impression I got.
I seem to remember seeing it stated somewhere in a book I was reading in the library, and then reverse-...
- 7,329
5
votes
1
answer
514
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Request for reference: Banach-type spaces as algebraic theories.
Sparked by Yemon Choi's answer to Is the category of Banach spaces with contractions an algebraic theory? I've just spent a merry time reading and doing a bit of reference chasing. Imagine my delight ...
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