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17 votes
3 answers
905 views

Existence of translation-invariant basis on $C_c(\mathbb R)$

Consider the space $C_c(\mathbb R)$ of complex-valued continuous functions of compact support. This is a vector space over $\mathbb C$, and I am not considering any topology, so the question is ...
Nick S's user avatar
  • 2,071
9 votes
2 answers
338 views

Does $End(V)$ remember $V$, where $V$ is a locally convex space?

Let $V$ be a locally convex topological vector space over $\mathbb C$, and let $A=\mathrm{End}(V)$ be its algebra of continuous linear endomorphisms (viewed just as a $\mathbb{C}$-algebra, not as a ...
André Henriques's user avatar
2 votes
0 answers
216 views

Separating duality for TVS?

What is the modern concept (term) for "separating duality" (dualité séparante in french) in the sense of Bourbaki (TVS Ch II § 6) as explained in the following ? ...
Duchamp Gérard H. E.'s user avatar
0 votes
2 answers
415 views

Commutative *-subrings of the noncommutative C*-algebra $B(l^2)$

A $\star$-ring is a ring with an involutive anti-automorphism. The simplest example of a noncommutative $\star$-ring is perhaps $B(l^2)$, the ring of bounded linear functions on the sequence space $l^...
user avatar
2 votes
0 answers
520 views

Eigenvector of infinite matrix

I consider the system of reaction-diffusion PDEs in a ball with Robin boundary condition. It is a Steklov eigenvalue problem (see G Auchmuty (2004) "Steklov eigenproblems and the representation of ...
Szopa's user avatar
  • 31