Showing an operator is compact
8698
Show the Volterra Operator is compact using only the definition of compact
55067
Norm of self-adjoint operator
22394
Compact operator maps weakly convergent sequences into strongly convergent sequences
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
124959
Does weak compactness imply boundedness in a normed vector space (not necessarily complete)?
104097
An idempotent operator is compact if and only if it is of finite rank
144019
A strictly positive operator is invertible
45071
Having the derivative be an operator
47668
Show that $lim_{n \rightarrow \infty}m(O_n)=m(E)$ when $E$ is compact.
132491
How to show that $C=C[0,1]$ is a Banach space
125776
If space of bounded operators L(V,W) is Banach, V nonzero, then W is Banach (note direction of implication)
9268
Proving that the Union of Two Compact Sets is Compact
69497
Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$
147213
Prove that finite unions of compact sets are compact
144104
Show that a positive operator on a complex Hilbert space is self-adjoint
46265
Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$
131906
"An operator is hermitian". Implications?