On a commutator theorem of robert c. thompson

1984 ◽  
Vol 16 (1-4) ◽  
pp. 129-131 ◽  
Author(s):  
L. Grunenfelder ◽  
R. Paré ◽  
H. Radjavi
Keyword(s):  
Commutator Theorem

d-dimensional orthogonal polynomials: Commutator theorem and other results

2017 ◽  
Vol 20 (02) ◽  
pp. 1750011
Author(s):  
Luigi Accardi ◽  
Abdallah Dhahri
Keyword(s):  
Orthogonal Polynomials ◽  
Random Variable ◽  
Product Measure ◽  
Classical Formula ◽  
Variable Formula ◽  
Commutator Theorem ◽  
The Creation ◽  
New Formulation ◽  
Preservation Operator

We give new and simplified proofs of three basic theorems in the theory of orthogonal polynomials associated to a classical, [Formula: see text]-valued random variable [Formula: see text] with all moments, namely: (1) The characterization of [Formula: see text] in terms of commutators among the creation–annihilation–preservation (CAP) operators in its quantum decomposition. (2) The characterization, in terms of the same objects, of the fact that the distribution of [Formula: see text] is a product measure. (3) The equivalence of the symmetry of [Formula: see text] with the vanishing of the associated preservation operator. Our new formulation of these results allows one to obtain a stronger form of the above statements.

scholarly journals Commutators in real interpolation with quasi-power parameters

2002 ◽  
Vol 7 (5) ◽  
pp. 239-257 ◽  
Author(s):  
Ming Fan
Keyword(s):  
Function Spaces ◽  
Higher Order ◽  
Real Interpolation ◽  
Hardy Inequalities ◽  
Commutator Estimates ◽  
The Real ◽  
Interpolation Methods ◽  
Commutator Theorem

The basic higher order commutator theorem is formulated for the real interpolation methods associated with the quasi-power parameters, that is, the function spaces on which Hardy inequalities are valid. This theorem unifies and extends various results given by Cwikel, Jawerth, Milman, Rochberg, and others, and incorporates some results of Kalton to the context of commutator estimates for the real interpolation methods.

scholarly journals A quantitative version of the commutator theorem for zero trace matrices

2012 ◽  
Vol 110 (48) ◽  
pp. 19251-19255 ◽  
Author(s):  
W. B. Johnson ◽  
N. Ozawa ◽  
G. Schechtman
Keyword(s):  
Quantitative Version ◽  
Commutator Theorem

scholarly journals A commutator theorem for fractional integrals in spaces of homogeneous type

2000 ◽  
Vol 24 (6) ◽  
pp. 403-418 ◽  
Author(s):  
Jorge J. Betancor
Keyword(s):  
Fractional Integrals ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Commutator Theorem

We give a new proof of a commutator theorem for fractional integrals in spaces of homogeneous type.

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