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 2011 (vol 56 pp. 593)
|On the $p$-norm of an Integral Operator in the Half Plane|
We give a partial answer to a conjecture of DostaniÄ on the determination of the norm of a class of integral operators induced by the weighted Bergman projection in the upper half plane.
Keywords:Bergman projection, integral operator, $L^p$-norm, the upper half plane
Categories:47B38, 47G10, 32A36
3. CMB 2011 (vol 55 pp. 762)
|Smooth Approximation of Lipschitz Projections|
We show that any Lipschitz projection-valued function $p$ on a connected closed Riemannian manifold can be approximated uniformly by smooth projection-valued functions $q$ with Lipschitz constant close to that of $p$. This answers a question of Rieffel.
Keywords:approximation, Lipschitz constant, projection
4. CMB 2010 (vol 53 pp. 398)
|Projections in the Convex Hull of Surjective Isometries|
We characterize those linear projections represented as a convex combination of two surjective isometries on standard Banach spaces of continuous functions with values in a strictly convex Banach space.
Keywords:isometry, convex combination of isometries, generalized bi-circular projections
Categories:47A65, 47B15, 47B37
5. CMB 2009 (vol 52 pp. 403)
|Shaken Rogers's Theorem for Homothetic Sections |
We shall prove the following shaken Rogers's theorem for homothetic sections: Let $K$ and $L$ be strictly convex bodies and suppose that for every plane $H$ through the origin we can choose continuously sections of $K $ and $L$, parallel to $H$, which are directly homothetic. Then $K$ and $L$ are directly homothetic.
Keywords:convex bodies, homothetic bodies, sections and projections, Rogers's Theorem
6. CMB 2005 (vol 48 pp. 69)
|Biorthogonal Systems in Weakly LindelÃ¶f Spaces |
We study countable splitting of Markushevich bases in weakly Lindel\"of Banach spaces in connection with the geometry of these spaces.
Keywords:Weak compactness, projectional resolutions,, Markushevich bases, Eberlein compacts, Va\v sÃ¡k spaces
Categories:46B03, 46B20., 46B26