# Questions tagged [unbounded-operators]

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### Operator-form correspondence without lower semiboundedness

When dealing with a normal unbounded operator $A$, it is often useful to frame questions about the operator in terms of questions about the associated form $\omega,$ which has domain $D(|A|^{1/2})$ ...
• 109
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### Perturbation of one-parameter groups of unitary operators

Let $H$ be a Hilbert space and let $h$ be a fixed, densely defined, possibly unbounded, self-adjoint operator on $H$. Letting $B(H)$ denote the space of all bounded operators on $H$, it is well ...
• 2,263
1 vote
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### Everywhere-defined unbounded operators between Banach spaces

In this post, it is said that there are no constructive examples of everywhere-defined unbounded operators between Banach spaces; every example furnished must use the axiom of choice. This seems like ...
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• 145
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### How to prove the polar decomposition of unbounded operators?

Let $T$ be a closed, densely defined operator on a Hilbert space $H$. Then there exists a positive self-adjoint operator $A$, $D(A)=D(T)$ and a isometric operator $V:R(A)\to \overline{R(T)}$ ...
• 1,187
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### Closure of the point spectrum of an unbounded diagonalizable operator

Given a (separable) Hilbert space H and an unbounded densely defined linear operator $T:{\cal D}(T) \to$H such that ${\cal D}$ is diagonalizable (it means $\exists$ an O.N.B. of H such that all basis ...
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• 969
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### Power of an infinitesimal generator of a $C_0$-semigroup in a Banach space
Let $A$ be the infinitesimal generator of a $C_0$-semigroup of linear operators in a Banach space. Let $n$ be a positive integer, $n\geq2$. Is $A^n$ closed? Here (setting $A^1$ $:=$ $A$, and ...
Let $\mathbf{H}$ be a Hilbert space, and $D$ an unbounded densely-defined operator on $\mathbf{H}$. As is well-known, every such operator admits an adjoint, with domain possibly different from that ...