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 this was proved for finite-dimensional
Symmetric norms and spaces of operatorsdoi:10.1007/978-3-319-18796-9_15Fritz GesztesyGilles GodefroyLoukas GrafakosIgor VerbitskySpringer International Publishing
Symmetric norms and spaces of operators 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 a... NJ Kalton,FA Sukochev - 《Journal Für Die Reine Und Angewandte Mathematik》 被引量: ...
{T}\right) $, and we extend many of the classical results, including the dominated convergence theorem, convolution theorems, dual spaces, Beurling-type invariant spaces, inner-outer factorizations, characterizing the multipliers and the closed densely-defined operators commuting with multiplication by ...
The problem of characterizing all admissible quasi-norms c and all pseudo-isotropic measures in M(c) remains an open and difficult question, except for a few cases. It is strictly connected with characterizing all extreme points in the set M(c). One possible approach for solving the characteri...
Analysis on heat kernel has been an active research area for a long time in analysis, geometry and probability. A central topic of the area is to obtain global quantitative bounds on the heat kernel. Nash-type inequalities can effectively characterize upper bounds of the operator norms of semi...
[10]. In the above it is important to note that C is conjugate-linear and thus the study of complex symmetric operators is quite distinct from that of operators on indefinite inner product spaces. As a simple example, consider the Volterra integration operator T : L 2 [0, 1] →L 2...
thisarticlewedeterminetheimageofthistransformonL2.1.IntroductionTheheatequation,andtheassociatedheatkerneltransform(alsoknownastheBargmann-Segaltrans-form),isanaturalcounterpartofaRiemannianmetric.ForthehomogeneousspacesRnoracompactsymmetricspaceendowedwiththeusualmetric,manypropertiesoftheheatkerneltransformareknown[2,9...
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...
In the case of multiplier operators on Td, d≥2, Theorem 2 follows from Corollary 1 and [22, Theorem 1]. Observe that Corollary 2 gives sharp lower bounds for dnWpγMd,LqMd on two-point homogeneous spaces Md if 1<q≤p<∞, 2≤q≤p<∞, γ>0 which are new in the case 1<q≤...