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1. CMB Online first
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)
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)
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)
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 |