We show that if (E,∥·∥E) is a symmetric Banach sequence space then the corresponding space of operators on a separable Hilbert space, defined by if and only if , is a Banach space under the norm . Although t
Symmetric norms and spaces of operatorsdoi:10.1007/978-3-319-18796-9_15Fritz GesztesyGilles GodefroyLoukas GrafakosIgor VerbitskySpringer International Publishing
Kalton, N.J., Sukochev, F.A.: Symmetric norms and spaces of operators. J. Reine Angew. Math. 621, 81–121 (2008) MathSciNet MATH Google Scholar Krengel, U.: Ergodic Theorems. Walter de Gruyer, Berlin (1985) Book Google Scholar Litvinov, S.: Uniform equicontinuity of sequences...
, and that there is an equality of norms f 2 = a (DO |Htf| 2)(iY ) w t (Y )dY, the weight function w t being given by w t (Y ) = 1 |W| · e 2t|ρ| 2 (2πt) n/2 · e −|Y | 2 2t (Y ∈ a), W the usual Weyl group and n = rankX. To describe imH...
Since all norms are equivalent on the finite dimensional Banach space A k , there exists a positive constant C A k such that ∥ ξ ∥ L p 2 ( Ω ) ≥ C A k ∥ ξ ∥ X 0 . Then for ∥ ξ ∥ X 0 = ρ k ≥ 1 , from (28), we have I ( ξ ) : = 1 b p 2 a...
In addition, there exists C=C(M)>1 depending onM:=(infa)−1+(infb)−1+‖a‖∞+‖b‖∞+‖c‖∞+‖d‖∞, where the infima and norms are taking over r∈[0,1], such that, for all v∈D(L) and λ∈C such that Reλ⩾C(M), we have(3.10)|λ|‖v‖∞+|λ|1/2‖...
We show that if (, ∥·∥) is a symmetric Banach sequence space then the corresponding spaceof operators on a separable Hilbert space, defined byif and only if, is a Banach space under the norm. Although this was proved for finite-dimensional spaces by von Neumann in 1937, it has never...
It is proved in [14] and [15] that for each weakly 2 -summable sequence ( x n ) in E the sequence (║ x n ║ p ) of norms in ℓ p is a multiplier from ℓ p into E. This result is a proper improvement of well-known analogues in ℓ p -spaces due to Littlewood, ...
We also prove a duality theorem for a version of $L^{\\\alpha}$ in the setting of von Neumann algebras.doi:10.48550/arXiv.1407.7920Yanni Cheneprint arxivY. Chen, Lebesgue and Hardy spaces for symmetric norms I, arXiv: 1407.7920 [math. OA] (2014).Y...
symmetric tensor productantisymmetric tensor productHilbert spaceHardy spacesWe study symmetric and antisymmetric tensor products of Hilbert-space operators, focusing on norms and spectra for some well-known classes favored by function-theoretic operator theorists. We pose many open qu...