1998/11/24 by Peter G. Casazza, Casazza, Peter G.
Mathematics · #46B20 #46C05 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B20 #msc:46C05
paper · pdf · doi:10.48550/arxiv.math/9811148
to appear: J. of Fourier Anal. and Appl's
arxiv created 1998/11/24 · arxiv updated 2009/11/30
We show that every frame for a Hilbert space H can be written as a (multiple of a) sum of three orthonormal bases for H. A result of N.J. Kalton is included which shows that this is best possible in that: A frame can be represented as a linear combination of two orthonormal bases if and only if it is a Riesz basis. We further show that every frame can be written as a (multiple of a) sum of two normalized tight frames or as a sum of an orthonormal basis and a Riesz basis for H. Finally, every frame can be represented as a (multiple of a) average of two orthonormal bases for a larger Hilbert space.