Generalized Bochner theorem and Levy-Khinchine representation for completely positive definite generalized Toeplitz kernels

1997 ◽  
Vol 27 (4) ◽  
pp. 401-418
Author(s):  
Pedro Alegria
Keyword(s):  
Positive Definite ◽  
Completely Positive ◽  
Bochner Theorem

scholarly journals Positive definite functionals in Banach spaces

1977 ◽  
Vol 23 (4) ◽  
pp. 416-420
Author(s):  
G. G. Hamedani
Keyword(s):  
Banach Spaces ◽  
Positive Definite ◽  
Bochner Theorem

AbstractWe establish a version of Bochner Theorem due to S. Boylan for Banch spaces with a basis.

scholarly journals The index of product systems of Hilbert modules: Two equivalent definitions

2015 ◽  
Vol 97 (111) ◽  
pp. 49-56
Author(s):  
Biljana Vujosevic
Keyword(s):  
Positive Definite ◽  
Hilbert Modules ◽  
Product System ◽  
Initial Product ◽  
Positive Definite Kernel ◽  
Completely Positive ◽  
C Algebra ◽  
Product Systems ◽  
The One ◽  
Definition Of

We prove that a conditionally completely positive definite kernel, as the generator of completely positive definite (CPD) semigroup associated with a continuous set of units for a product system over a C*-algebra B, allows a construction of a Hilbert B?B module. That construction is used to define the index of the initial product system. It is proved that such definition is equivalent to the one previously given by Keckic and Vujosevic [On the index of product systems of Hilbert modules, Filomat, to appear, ArXiv:1111.1935v1 [math.OA] 8 Nov 2011]. Also, it is pointed out that the new definition of the index corresponds to the one given earlier by Arveson (in the case B = C).

scholarly journals ON ITERATED POWERS OF POSITIVE DEFINITE FUNCTIONS

2015 ◽  
Vol 92 (3) ◽  
pp. 440-443
Author(s):  
MEHRDAD KALANTAR
Keyword(s):  
Compact Group ◽  
Strong Operator Topology ◽  
Positive Definite Function ◽  
Positive Definite ◽  
Locally Compact Group ◽  
Definite Function ◽  
Completely Positive Maps ◽  
Locally Compact ◽  
Completely Positive ◽  
Positive Maps

We prove that if ${\it\rho}$ is an irreducible positive definite function in the Fourier–Stieltjes algebra $B(G)$ of a locally compact group $G$ with $\Vert {\it\rho}\Vert _{B(G)}=1$, then the iterated powers $({\it\rho}^{n})$ as a sequence of unital completely positive maps on the group $C^{\ast }$-algebra converge to zero in the strong operator topology.

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