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A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.

5 votes
1 answer
391 views

What Approximation Property does the space of Schatten-p class operators have?

Background This is a follow-up question to: What (classes of) Banach spaces are known to have Schauder basis? In the previous question, I asked about what spaces are known to have Schauder basis. It …
Clark Chong's user avatar
16 votes
1 answer
2k views

What (classes of) Banach spaces are known to have Schauder basis?

Motivation: I am trying to see for what class of Banach spaces the following result is true: There exists an increasing sequence of finite dimensional subspace {$V_n$} of a Banach space X (with so …
Clark Chong's user avatar
0 votes
0 answers
184 views

Can I define Fredholm Index using $\dim \ker ST - \dim \ker TS$?

$X$, $Y$ are Banach spaces. Let $S \in L(X, Y)$, $T \in L(Y, X)$, where $L(X, Y)$ denotes the Banach algebra of bounded linear operators from $X$ to $Y$. If we have that $Id_Y - ST \in \mathbb{K}(Y)$ …
Clark Chong's user avatar