@MISC{Oikhberg97productsof, author = {Timur Oikhberg}, title = {Products Of Orthogonal Projections}, year = {1997} }

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Abstract

. We give a characterization of operators on a separable Hilbert space of norm less than one that can be represented as products of orthogonal projections and give an estimate on the number of factors. We also describe the norm closure of the set of all products of orthogonal projections. 1. Introduction. In this paper, we study products of orthogonal projections on separable (finite or infinite dimensional) Hilbert spaces. Throughout the work, the word projection is reserved to orthogonal projections on a Hilbert space. The word idempotent refers to a (not necessarily orthogonal) projection. The problem of describing operators acting on a finite dimensional complex Hilbert space which can be represented as products of orthogonal projections was solved by Kuo and Wu. In [KW1] they proved that u : # n 2 # # n 2 is a product of projections if and only if either u is the identity map or u = I m#S, where I m is the identity on an m-dimensional subspace of # n 2 and S is a singular...