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Results tagged with banach-spaces
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user 45494
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
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Self-Adjointness for Banach Spaces
Good evening. Is there a reasonable notion of being self-adjoint for the adjoint operator on Banach Spaces? Kind regards, Alex
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Compact Approximation
This thread originated from MSE: Compact Approximation
This is meant as lemma for: Approximation Property
Given a Banach space $E$.
Denote compact domains by $\mathcal{C}$.
Denote compact operator …
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Approximation Property: Characterization
Problem
Given a Banach space $E$. Denote compact sets by $\mathcal{C}$, compact operators by $\mathcal{C}(X,Y)$, and finite rank operators by $\mathcal{F}(X,Y)$.
Suppose it has the approximation pro …
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4
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Differentiability: Partially Defined Functions
These ideas came to my mind while reading Lee's Introduction to Smooth Manifolds.
(Cf. discussion on p. 45.)
Definition
Let $E$ and $F$ be two Banach spaces together with a plain subset $A\subsete …
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answer
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Approximation Property: Decomposition
This thread originated from MSE: Approximation Property: Decomposition
Given a Banach space $E$.
Consider a finite rank operator $F\in\mathcal{F}(X,E)$.
Introduce a basis on the finite dimensional …
- 598
2
votes
Differentiability: Partially Defined Functions
1.(Riesz-Dunford Functional Calculus)
Consider the function $f(z):=|z|^2$ defined on the real and imaginary axis only. Then around every point it has an extension to a continuously differentiable fun …
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