Abstract
A quite general theorems on unconditional bases in separable Hilbert spaces, given in terms of values of entire operator valued vector-functions, were established in the papers [2–4]. In the present paper, we give a detailed analysis of the hypothesis of these theorems. We present examples of various classes of vector-functions that satisfy some of the hypothesis of the above theorems. On the other hand, we show that there exist natural classes of vector-functions that do not satisfy some of the hypothesis of Theorem A.
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Gennadiy Gubreev: Deceased.
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Gubreev, G., Tarasenko, A. On the theory of unconditional bases of Hilbert spaces formed by entire vector-functions. Bol. Soc. Mat. Mex. 24, 269–278 (2018). https://doi.org/10.1007/s40590-016-0153-3
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DOI: https://doi.org/10.1007/s40590-016-0153-3