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Results tagged with fa.functional-analysis
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user 5734
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
4
votes
Orthogonality in non-inner product spaces
Concerning your follow-up question (iii) there is the following very nice result: For Birkhoff-James orthogonality
it is easy to find examples where $y\perp x$ but
$\left\|x\right\|/\left\|x+\alpha …
- 2,545
7
votes
Accepted
Continuity of the involution in Banach *-algebras
For 1), this is § 36 (pp. 190) of Bonsall & Duncan: The following are equivalent for a Banach *-algebra $A$, and the set $\text{Sym}(A')$ of all continuous self-adjoint linear functionals on $A$
Th …
- 2,545
4
votes
positive functional on Banach *-algebra (with appro. identity) is continuous?
F. F. Bonsall & J. Duncan, Complete Normed Algebras, Springer 1973: §37, Star Representations and Positive Functionals, Theorem 15 (p. 201).
Let $A$ (a Banach star algebra) have a bounded two-sided a …
- 2,545
3
votes
Accepted
A nilpotency question on $C^{*}$ algebras
I'm not sure if this is useful: If your $C^*$-algebra also has a non-zero nilpotent element, then it will have nilpotent elements of all orders, it is not (algebraically) of bounded index, so does not …
- 2,545
1
vote
Reference for "Every compact quasinilpotent operator is the limit of nilpotent ones"
Halmos's BAMS paper's references include: R. G. Douglas and Carl Pearcy, A note on quasitriangular operators, Duke Math. J. 37 (1970), 177–188.
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