Unconditional bases in radial Hilbert spaces

2022 ◽  
Vol 86 (1) ◽  
Author(s):  
Konstantin Petrovich Isaev ◽  
Rinad Salavatovich Yulmukhametov
Keyword(s):  
Hilbert Spaces ◽  
Unconditional Bases

Equivalent Norms in Hilbert Spaces with Unconditional Bases of Reproducing Kernels

2020 ◽  
Vol 250 (2) ◽  
pp. 310-321
Author(s):  
K. P. Isaev ◽  
K. V. Trunov ◽  
R. S. Yulmukhametov
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernels ◽  
Equivalent Norms ◽  
Unconditional Bases

scholarly journals Geometry of radial Hilbert spaces with unconditional bases of reproducing kernels

2020 ◽  
Vol 12 (4) ◽  
pp. 55-63
Author(s):  
Konstantin Petrovich Isaev ◽  
Rinad Salavatovich Yulmukhametov
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernels ◽  
Unconditional Bases

scholarly journals Unconditional bases in tensor products of Hilbert spaces

2005 ◽  
Vol 96 (2) ◽  
pp. 280 ◽  
Author(s):  
David Pérez-García ◽  
Ignacio Villanueva
Keyword(s):  
Recent Result ◽  
Hilbert Spaces ◽  
Unconditional Basis ◽  
Classical Result ◽  
Tensor Products ◽  
Unconditional Bases ◽  
Schmidt Norm ◽  
Symmetric Version ◽  
Tensor Norm

We prove that a tensor norm $\alpha$ (defined on tensor products of Hilbert spaces) is the Hilbert-Schmidt norm if and only if $\ell_2\otimes\cdots\otimes \ell_2$, endowed with the norm $\alpha$, has an unconditional basis. This extends a classical result of Kwapień and Pełczyński. The symmetric version of that statement follows, and this extends a recent result of Defant, Díaz, García and Maestre.

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