On Sub-Gaussianity in Banach Spaces - Giorgobiani, George; Kvaratskhelia, Vakhtang; Tarieladze, Vazha (Mathematical Problems of Computer Science, 2024)
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.