Contractivity of positive and trace-preserving maps under Lp norms

0 An Analysis of Completely - Positive Trace - Preserving Maps

We give a useful new characterization of the set of all completely positive, trace-preserving maps Φ : M2 → M2 from which one can easily check any trace-preserving map for complete positivity. We also determine explicitly all extreme points of this set, and give a useful parameterization after reduction to a certain canonical form. This allows a detailed examination of an important class of non...

Norms of Positive Operators on LP-Spaces

Let 0 < T: LP(Y, v) -+ Lq(X, ) be a positive linear operator and let HITIP ,q denote its operator norm. In this paper a method is given to compute 1Tllp, q exactly or to bound 11Tllp q from above. As an application the exact norm 11VIlp,q of the Volterra operator Vf(x) = fo f(t)dt is computed.

A Survey of Invertibility and Spectrum Preserving Linear Maps

0 A Characterization of Completely - Positive Trace - Preserving Maps on M 2

We give a useful new characterization of the set of all completely positive, trace-preserving maps Φ : M2 → M2. This allows us to determine explicitly all extreme points of this set, and to easily check any tracepreserving map for complete positivity. We also find an interesting class of extreme channels which appear to be new.

N ov 2 00 1 An Analysis of Completely - Positive Trace - Preserving Maps

We give a useful new characterization of the set of all completely positive, trace-preserving maps Φ : M2 → M2 from which one can easily check any trace-preserving map for complete positivity. We also determine explicitly all extreme points of this set, and give a useful parameterization after reduction to a certain canonical form. This allows a detailed examination of an important class of non...