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10 papers · 1 filter
Infinite dimensional restricted invertibility
Peter G. Casazza, Goetz E. Pfander
The 1987 Bourgain-Tzafriri Restricted Invertibility Theorem is one of the most celebrated theorems in analysis. At the time of their work, the authors raised the question of a poss…
Generalized Polar Decompositions for Closed Operators in Hilbert Spaces and Some Applications
Fritz Gesztesy, Mark Malamud, Marius Mitrea +1
We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (f…
A new approach to the Ramsey-type games and the Gowers dichotomy in F-spaces
G. Androulakis, S. J. Dilworth, N. J. Kalton
We give a new approach to the Ramsey-type results of Gowers on block bases in Banach spaces and apply our results to prove the Gowers dichotomy in F-spaces.
The complex Busemann-Petty problem on sections of convex bodies
A. Koldobsky, H. König, M. Zymonopoulou
The complex Busemann-Petty problem asks whether origin symmetric convex bodies in $\C^n$ with smaller central hyperplane sections necessarily have smaller volume. We prove that the…
A Decomposition Theorem for frames and the Feichtinger Conjecture
Peter G. Casazza, Gitta Kutyniok, Darrin Speegle +1
In this paper we study the Feichtinger Conjecture in frame theory, which was recently shown to be equivalent to the 1959 Kadison-Singer Problem in -Algebras. We will show th…
Invertibility of random matrices: norm of the inverse
Mark Rudelson
Let A be an n by n matrix, whose entries are independent copies of a centered random variable satisfying the subgaussian tail estimate. We prove that the operator norm of A^{-1} do…