All Questions
Tagged with fa.functional-analysis reference-request
1,021 questions
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 ...
- 1,649
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 ...
- 1,411
23
votes
5
answers
6k
views
Hahn-Banach without Choice
The standard proof of the Hahn-Banach theorem makes use of Zorn's lemma. I hear that, however, Hahn-Banach is strictly weaker than Choice. A quick search leads to many sources stating that Hahn-Banach ...
- 1,202
7
votes
2
answers
2k
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Heat kernel estimates and Gaussian estimates for semigroups, good reference?
Hi, it seems like a big field and I'm having trouble getting some solid/classic references to get me started.
If $U \subset \mathbb{R}^d$ is a bounded domain with, say, $C^2$-boundary $\partial U$ ...
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 ...
- 29.8k
4
votes
3
answers
1k
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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 ...
- 1,284
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 ...
- 8,512
2
votes
2
answers
602
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Reference for weak*-semigroup
Let $X$ a dual Banach space (there exists a Banach space $Y$ such that $X=Y'$).
A weak* semigroup on $X$ is a semigroup $(T_t)_{\geq 0}$ on $X$ such that, for all $x\in X$, we have $T_tx\to x$ in the ...
- 1,222
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 ...
- 1,222
16
votes
3
answers
791
views
Random products of projections: bounds on convergence rate?
The von Neumann-Halperin [vN,H] theorem shows that iterating a fixed product of projection operators converges to the projector onto the intersection subspace of the individual projectors. A good ...
- 181
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 ...
8
votes
1
answer
920
views
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 ...
- 5,515
5
votes
2
answers
579
views
Improved versions of discontinuous functions
Given a set X (such as the set of points in an interval), the space ℝX of all real-valued functions on X is not usually the function space we work with -- it is "too large" in some sense. Thus, ...
- 8,903
1
vote
2
answers
3k
views
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 ...
- 51
7
votes
2
answers
2k
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What is the "Krein-Milman theorem for cones"?
Update: The question is completely answered. I had overlooked a reduction to the self-adjoint case, and the latter can be proved using a Hahn-Banach separation theorem. Thanks to Matthew Daws for ...
- 7,329
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 ...
- 4,060
4
votes
3
answers
3k
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Examples of Banach spaces and their duals
There are many representation theorems which state that the dual space of a Banach space $X$ has a particularly concrete form. For example, if $X = C([0,1],\mathbb R)$ is the space of real-valued ...
- 8,512
32
votes
19
answers
23k
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Good books on theory of distributions
Hi all.
I'm looking for english books with a good coverage of distribution theory.
I'm a fan of Folland's Real analysis, but it only gives elementary notions on distributions.
Thanks in advance.
6
votes
1
answer
1k
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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-...
- 25.8k
32
votes
11
answers
23k
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A book for problems in Functional Analysis
I want to know if there's any book that categorizes problems by subjects of Functional Analysis.
I'm studying Functional Analysis now a days and I really need to solve some problems in order to ...
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 ...
- 26.8k