Uncountable Frames in Non-Separable Hilbert Spaces and their characterization

M. I. Ismailov, Z. V. Mamedova, 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 defined,
their properties are studied. Many results related to usual frames are extended
to new case. Examples are given.


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