Uncountable Frames in Non-Separable Hilbert Spaces and their Characterization

B. T. Bilalov, M. I. Ismailov, Y. I. Nasibov


The concepts of Bessel families and frames in non-separable Hilbert spaces are introduced in this work. Besselianness criterion for a family is found. Similar to the usual case, analysis,
synthesis and frame operators are dened, their properties are studied. Many results related to
usual frames are extended to new case. Examples are given.


non-separable space, Bessel family, uncountable frame


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