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Showing the following subset of the dual space is compact

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#functional-analysis #weak-topology
63
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Definition of weak-star topology of bounded linear maps from space to dual of other space

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#functional-analysis #weak-topology
95
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TVS Completion of Banach space wrt weak topology

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#functional-analysis #topological-vector-spaces #weak-topology
59
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Exercise 3.19 in Brezis' Functional Analysis

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#calculus #sequences-and-series #functional-analysis #weak-convergence #weak-topology
109
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Existence of a weak-star limit of a family of operators in $B(\mathcal{H})$

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#functional-analysis #operator-theory #operator-algebras #semigroup-of-operators #weak-topology
57
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Is this comment about weak convergence in $W^{1,2}(\Omega)$ correct?

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#functional-analysis #sobolev-spaces #compact-operators #weak-topology
31
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The map $T: (H^1 (I), \|\cdot\|_{L^2}) \to \mathbb R, u \mapsto \|u\|_{H^1}$ is lower semi-continuous

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#functional-analysis #solution-verification #continuity #sobolev-spaces #weak-topology
65
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Proof verification regarding weak-continuity

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#functional-analysis #weak-topology
41
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Exercise 3.1.23 in Salamon's Functional Analysis

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#functional-analysis #weak-convergence #weak-topology
62
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Extension of a continuous function $f:X\rightarrow X$ to a function $g: E\rightarrow E$ such that $X$ is embedded in $E$, a Banach space.

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#general-topology #functional-analysis #metric-spaces #dynamical-systems #weak-topology
44
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Prove $X$ has the weak topology where $p:X\to Y$ is a covering map.

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#algebraic-topology #covering-spaces #cw-complexes #weak-topology
225
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Definition of weak convergence

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#general-topology #banach-spaces #weak-convergence #dual-spaces #weak-topology
55
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Does weak $L^2$ approximation implies $L^2$ approximation under a condition similar to convexity?

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#functional-analysis #measure-theory #hilbert-spaces #weak-convergence #weak-topology
55
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How does the weak topology imply the definition of weak convergence?

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#functional-analysis #banach-spaces #weak-convergence #dual-spaces #weak-topology
100
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Consider the weak topology induced by all linear functionals. Is it determined on finite dimensional subspaces?

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#functional-analysis #topological-vector-spaces #weak-topology

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