# Tagged Questions

Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

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### Trivial intersection of kernels

This is a follow up to the question: Biorthogonal functionals. A positive answer to that question implies a negative answer to this one. If $X$ is a separable Banach space, can we find a basic ...
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### $id:A\to A^{op}$ is completely positive iff $A$ is abelian

Let $A$ be a $C^*$-algebra and $A^{op}$ it's opposite $C^*$-algebra. Let $id:A\to A^{op}$ be the identity map. $id$ is positive. The claim is: $id$ is completely positive iff $A$ is abelian. I need ...
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### Biorthogonal functionals

If $X$ is a separable Banach space and $(x_n)$ is a basic sequence, then we can define biorthogonal functionals $(x^{*}_n)$ in $X^{*}$ such that $x^{*}_n(x_k)=\delta_{nk}$. What about conversely? If ...
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### Negative eigenvalue of Toeplitz Hermitian matrix?

I am working on estimation of a covariance matrix and I know that the matrix is Toeplitz. The desired matrix should not produce negative eigenvalues at all. However, sometime my estimation leads to a ...
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### Linear functions

Let $(f_1, f_2, \ldots, f_n)$ be an $n$-tuple of functions mapping non-negative integers to non-negative integers. Let $m$ be a positive integer.Suppose there exists a function $f$ apping non-negative ...
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If an operator $A$ on a Hilbert space $H$ generates a strongly continuous semigroup, does then the operator $B$ on $H \oplus H$ given by the matrix $$B := \begin{pmatrix} 0 & \mathrm{id} \\ A &... 1answer 129 views ### Functional Calculus of closed operators I learned that there is a holomorphic functional calculus for closed operators: If T is a closed operator on a Hilbert space, and f is a function that is holomorphic on some open subset \Omega ... 1answer 211 views ### Fourier transform surjective on L^p(\mathbb{R}^n) for p \in (1,2)? I know that F_2:L^2 \rightarrow L^2 is of course unitary, whereas F_1:L^1 \rightarrow C_0 is injective but not surjective. This can be seen by looking at the dual map. Riesz-Thorin gives us that ... 0answers 52 views ### Isometry from a representation to the representation tensored with itself Suppose, the group  G=S(2^{\infty}) has a unitary representation  \pi  on a separable infinite dimensional Hilbert space  H . (The group  S(2^{\infty})  is the direct limit of the following ... 0answers 33 views ### Rademacher function and weakly p-summable sequence The function  r_{n}:[0,1]\rightarrow \lbrace -1,1\rbrace  be defined by  r_{n}(t):=sgn(sin(2^{n}\pi t)  is known as the n-th Rademacher function. is  (r_{n})  weakly p-summable sequence in ... 1answer 168 views ### Formula for an integration on \mathbb{Q} \cap [0,1] In order to work with functions defined on \mathbb{Q} \cap [0,1] I would like to define an adapted "integration" formula on this set. I though that following definition could be interesting:$$ \...
Consider an operator $T: L^2 \mapsto L^2$ of the form $TA = g (h \ast A)$ where $g$ is and $h$ are bounded $C^\infty$ functions. This operator $T$ can be shown to be Hilbert-Schmidt, hence compact. ...