All Questions
Tagged with operator-theory reference-request
190
questions
1
vote
1
answer
47
views
Unique extension of $*$-representation into an abstract multiplier algebra
I'm trying to find a proof of the following fact:
Let $A,B$ be $C^{*}$-algebras and $\pi: A \longrightarrow M(B)$ be a non-degenerate homomorphism in the sense that $\pi(A)B$ densely spans $B$. Then ...
- 1,399
2
votes
1
answer
112
views
Bishop's approximation theorem
I am trying to study the generalization that Axler made to Cuckovic work on the commutants of $T_{z^n}$ (Toeplitz operator with symbol $z^n$) on $L^{2}(\mathbb{D},dA)$, in the resource I am using, the ...
- 43
0
votes
0
answers
20
views
spectral theory of pseudo-differential operators of class $S^m$
I would be very grateful if you could give me the titles of books that deal with the spectral theory of pseudo-differential operators of class $S^m$
Thank you very much.
2
votes
0
answers
37
views
Reference request: uniformly continuous semigroups of nonlinear (Lipschitz) operators
Consider a Banach space $X$ with norm $\vert\cdot\vert$, and call an operator $A\colon X\to X$ Lipschitz whenever
$$\sup_{f\neq g} \frac{\vert Af-Ag\vert}{\vert f-g\vert}<+\infty;$$
the Lipschitz ...
- 21
1
vote
0
answers
15
views
What is the Propagator associated to a homogeneous Cauchy problem?
I came across this problem:
Consider the following Cauchy problem on $\mathbb{R}_t\times\mathbb{R}_x^n$
$$\begin{cases}\partial_tu+\omega\cdot\nabla_xu=f(t,x),\\ u|_{t=0}=u_0(x)\end{cases}$$
where $\...
- 598
0
votes
0
answers
46
views
Asking for reference about self adjointness
Is there someone that knows and can share any reference about the compactness and the self-adjointness of the operator
\begin{equation}
\pmb{\sigma}\cdot L
\end{equation}
on $H^1(\mathbb{R}^{3},\...
- 545
7
votes
1
answer
146
views
Trace Class Operators On Manifolds With Boundary
Let $X$ be an $n$-dimensional manifold with nonempty boundary $\partial X$ and $n\geq 2$. Proposition 4.1 of this paper by Schrohe states that it is "not very difficult" to show:
Proposition:...
- 2,508
0
votes
1
answer
55
views
Geometric and algebraic multiplicity of eigenvalues
Let $A$ be a closed operator on some Banach space $X$ and $\lambda \in \sigma_p(A)$. Then the dimension of the eigenspace $\ker(\lambda - A)$ is called the geometric multiplicity of $\lambda$. ...
- 5,137
1
vote
0
answers
37
views
Linear Algebra/Operator theory nomenclature or reference request
Given positive semidefinite operators $P,Q≥0$, is there a name for the operator $$S:=P^{1/2}Π₊(P^{1/2}QP^{1/2})P^{1/2},$$ where $$Π₊(P^{1/2}QP^{1/2})=\text {the projection onto the range of } P^{1/2}...
- 11
1
vote
0
answers
25
views
References for motivating the definition of a transfer operator
I am looking for references that motivative the following definition of a transfer operator from Wikipedia:
Let $X$ be an arbitrary set and $f: X\to X$. Then the transfer operator $\mathcal{L}$ is ...
- 1,221
5
votes
0
answers
42
views
Commutation of operators
Let $(\mathcal{H},\langle\cdot,\cdot\rangle)$ be a complex Hilbert space. Furthermore, let $E:\mathcal{D}(E)\to\mathcal{H}$ be a self-adjoint unbounded operator and $A:\mathcal{D}(A)\to\mathcal{H}$ (...
- 2,876
2
votes
1
answer
67
views
Does the ultra-weak topology coincide with the weak topology on the unit ball?
Just let me say first, I am no expert neither in $C^*$-algebras nor in $W^*$-algebras. But I came across the following question:
Let $A$ be a $C^*$-algebra. Then its bidual $A^{**}$ is also a $C^*$-...
- 5,137
0
votes
3
answers
43
views
Reference Request: the product of exponents of the same base is equivalent to the base raised to summation of the exponents
I am trying to find a reference and name for this property of big operators and exponents, but for the life of me I cannot find it anywhere.
$$\prod_{i=1}^{n} e^{x_i} = e^{\sum_{i=1}^n x_i}$$
Thank ...
- 1
1
vote
1
answer
50
views
Are there good bounds for the norm of a uniformly continuous semigorup $e^{tA}$ in terms of its generator $A$?
Are there good bounds for the norm of a uniformly continuous semigorup $e^{tA}$ in terms of its generator $A$? I'm only looking for references. In the standard literature, I wasn't able to find ...
- 13.9k
0
votes
0
answers
55
views
Looking for a paper of Harold Widom in 1990
Does anyone happen to have a copy of the paper
Widom, Harold, Eigenvalue distribution of nonselfadjoint Toeplitz matrices and the asymptotics of Toeplitz determinants in the case of nonvanishing index,...
- 11