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Results tagged with hilbert-spaces
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user 160051
A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.
5
votes
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answer
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An extension of Lomonosov Theorem
Let $H$ be a complex infinite dimensional separable Hilbert space. There are various extensions of the following well known result:
Theorem (Lomonosov): Every nonscalar $T \in B(H)$ which commutes wi …
- 1,175
3
votes
0
answers
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On a possible attempt to prove the invariant subspace problem
This question involves a possible method to prove the invariant subspace problem for (separable) infinite dimensional Hilbert spaces. The idea comes from various results on this topic; more precisely, …
- 1,175
1
vote
Accepted
An extension of Lomonosov Theorem
Looking again at Solution 12.4 in Kubrusly's book, I have noticed that the proof can be used even to prove the statement above, with some small changes. I will briefly sketch such small modifications: …
- 1,175
1
vote
0
answers
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On some bounds on two constants concerning the disconnectedness of the spectra of small pert...
Let $H$ be a separable, infinite dimensional, complex Hilbert space. In the book:
Jiang, C. L.; Wang, Z. Y. (1998). Strongly Irreducible Operators on Hilbert
Space. CRC press
above the statement of Th …
- 1,175