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arXiv · math/9812052

Symmetric approximation of frames and bases in Hilbert spaces

M. Frank·V. I. Paulsen·T. R. Tiballi
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Abstract

We consider existence and uniqueness of symmetric approximation of frames by normalized tight frames and of symmetric orthogonalization of bases by orthonormal bases in Hilbert spaces H . More precisely, we determine whether a given frame or basis possesses a normalized tight frame or orthonormal basis that is quadratically closest to it, if there exists such frames or bases at all. A crucial role is played by the Hilbert-Schmidt property of the operator (P-|F|), where F is the adjoint operator of the frame transform F*: H --> l_2 of the initial frame or basis and (1-P) is the projection onto the kernel of F. The result is useful in wavelet theory.

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BibTeXRIS

M. Frank, V. I. Paulsen, T. R. Tiballi. 1998-12-08. Symmetric approximation of frames and bases in Hilbert spaces. https://doi.org/10.2307/2693769

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