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Title:
On Sub-Gaussianity in Banach Spaces
Creator:
Giorgobiani, George J. ; Kvaratskhelia, Vakhtang V. ; Tarieladze, Vazha I.
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Uncontrolled Keywords:
Sub-Gaussian random variable ; Gaussian random variable ; weakly sub- Gaussian random element ; T−sub-Gaussian random element ; Hilbert space ; Banach space
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Abstract:
We show that if X is a Banach space and a weakly sub-Gaussian random element in X induces the 2-summing operator, then it is T−sub-Gaussian, provided that X is a reflexive type 2 space. Using this result, we obtain a characterization of weakly sub-Gaussian random elements in a Hilbert space which are T−sub-Gaussian.