A survey on dilations of projective isometric representations
Journal Title: Surveys in Mathematics and its Applications - Year 2008, Vol 3, Issue 0
Abstract
In this paper we present Laca-Raeburn's dilation theory of projective isometric representations of a semigroup to projective isometric representations of a group [M.Laca and I.Raeburn, Proc. Amer. Math. Soc., 1995] and Murphy's proof of a dilation theorem more general than that proved by Laca and Raeburn. Murphy applied the theory which involves positive definite kernels and their Kolmogorov decompositions to obtain the Laca-Raeburn dilation theorem [G.J. Murphy, Proc. Amer. Math.Soc., 1997]. <BR>We also present Heo's dilation theorems for projective representations, which generalize Stinespring dilation theorem for covariant completely positive maps and generalize to Hilbert C*-modules the Naimark-Sz-Nagy characterization of positive definite functions on groups [J.Heo, J.Math.Anal.Appl., 2007]. <BR>In the last part of the paper it is given the dilation theory obtained in [G.J. Murphy, Proc. Amer. Math.Soc., 1997] in the case of unitary operator-valued multipliers [Un Cig Ji, Young Yi Kim and Su Hyung Park, J. Math. Anal. Appl., 2007].
Authors and Affiliations
Tania Luminiţa Costache
Keywords
Related Articles
- EP ID EP97081
- DOI -
- Views 153
- Downloads 0
Ridge regression estimator: combining unbiased and ordinary ridge regression methods of estimation
Statistical literature has several methods for coping with multicollinearity. This paper introduces a new shrinkage estimator, called modified unbiased ridge (MUR). This estimator is obtained from unbiased ridge regressi...
Shock Waves in Gas Dynamics
Shock wave theory was studied in literature by many authors. This article presents a survey with references about various topics related to shock waves: Hyperbolic conservation laws, Well-posedness theory, Compactness th...
Multiple periodic solutions for a fourth-order discrete Hamiltonian system
By means of a three critical points theorem proposed by Brezis and Nirenberg and a general version of Mountain Pass Theorem, we obtain some multiplicity results for periodic solutions of a fourth-order discrete Hamiltoni...
Fixed points for multivalued contractions on a metric space
The purpose of this paper is to prove a fixed point theorem for multivalued operators and a fixed point theorem for multivalued weakly Picard operators in the terms of τ -distance.
Multivalued Perov-type theorems in generalized metric spaces
In this paper we present some fixed point results for multivalued operators, which extend the ones given by A.I. Perov and A.V. Kribenko, as well as some recent contributions due to A. Bucur, L. Guran and A. Petruşel.