On a factorization theorem of D. Lowdenslager

Authors:
V. Mandrekar and H. Salehi

Journal:
Proc. Amer. Math. Soc. **31** (1972), 185-188

MSC:
Primary 47.40; Secondary 42.00

MathSciNet review:
0287350

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Abstract: For a positive-definite infinite-dimensional matrixvalued function defined on the unit circle a factorization theorem for in the form , where is a function with Fourier series , is proved. The theorem, as was originally stated by D. Lowdenslager, contained an error. Based on our study concerning the completeness of the space of square-integrable operator-valued functions (not necessarily bounded) with respect to a nonnegative bounded operator-valued measure a correct proof of the factorization problem is provided. This work subsumes several known results concerning the factorization problem.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0287350-X

Keywords:
Hilbert space,
operator-valued functions and measures,
measurability,
generalized inverse factorization problem

Article copyright:
© Copyright 1972
American Mathematical Society