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Results tagged with operator-theory
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user 477203
Spectrum, resolvent, numerical range, functional calculus, operator semigroups. Special classes of operators: compact, Fredholm, dissipative, differential, integral, pseudodifferential, etc.
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Is $\Lambda:= \pi_2 \circ \pi_1:E \to L$ surjective?
Let $E$ be a Banach space. For a linear map $T$, we denote by $R(T)$ its range and by $N(T)$ its kernel. Let $I:E \to E$ be the identity map. Let $T:E \to E$ be a compact (bounded linear) operator. Th …
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Is $I-S$ in my attempt of Fredholm alternative injective?
Let $E$ be a Banach space. Let $\mathcal K(E)$ be the space of all compact (bounded linear) operators from $E$ to $E$. For a linear map $T$, we denote by $R(T)$ its range and by $N(T)$ its kernel. Let …
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Is $\Lambda:= \pi_2 \circ \pi_1:E \to L$ surjective?
A counter-example from this answer by Iosif Pinelis also works.
Indeed, suppose e.g. that $E=\mathbb R^2$ and
$$T=\begin{bmatrix}2&1\\ -1&0 \end{bmatrix};$$
here we will identify the linear operators …
- 657