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Search: MSC category 46C05 ( Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) )

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1. CMB 2013 (vol 57 pp. 463)

Bownik, Marcin; Jasper, John
Constructive Proof of Carpenter's Theorem
We give a constructive proof of Carpenter's Theorem due to Kadison. Unlike the original proof our approach also yields the real case of this theorem.

Keywords:diagonals of projections, the Schur-Horn theorem, the Pythagorean theorem, the Carpenter theorem, spectral theory
Categories:42C15, 47B15, 46C05

2. CMB 2012 (vol 57 pp. 42)

Fonf, Vladimir P.; Zanco, Clemente
Covering the Unit Sphere of Certain Banach Spaces by Sequences of Slices and Balls
e prove that, given any covering of any infinite-dimensional Hilbert space $H$ by countably many closed balls, some point exists in $H$ which belongs to infinitely many balls. We do that by characterizing isomorphically polyhedral separable Banach spaces as those whose unit sphere admits a point-finite covering by the union of countably many slices of the unit ball.

Keywords:point finite coverings, slices, polyhedral spaces, Hilbert spaces
Categories:46B20, 46C05, 52C17

3. CMB 2007 (vol 50 pp. 85)

Han, Deguang
Classification of Finite Group-Frames and Super-Frames
Given a finite group $G$, we examine the classification of all frame representations of $G$ and the classification of all $G$-frames, \emph{i.e.,} frames induced by group representations of $G$. We show that the exact number of equivalence classes of $G$-frames and the exact number of frame representations can be explicitly calculated. We also discuss how to calculate the largest number $L$ such that there exists an $L$-tuple of strongly disjoint $G$-frames.

Keywords:frames, group-frames, frame representations, disjoint frames
Categories:42C15, 46C05, 47B10

4. CMB 2002 (vol 45 pp. 60)

Dranishnikov, A. N.; Gong, G.; Lafforgue, V.; Yu, G.
Uniform Embeddings into Hilbert Space and a Question of Gromov
Gromov introduced the concept of uniform embedding into Hilbert space and asked if every separable metric space admits a uniform embedding into Hilbert space. In this paper, we study uniform embedding into Hilbert space and answer Gromov's question negatively.

Category:46C05

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