# Projective metrics and contraction principles for complex cones

## Related Articles

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Defines the Banach-Mazur distance for a pair of nonempty full dimensional bodies. Matrices utilized for the computation of Banach-Mazur distance; Theorem and proof of the computations; Vectors of a polyhedra shape; Discussion on Hilbert metric.

- The extreme points of a class of analytic operator-valued functions. HU Yuanyan; YI Yali; ZHOU Zewen // Journal of Huazhong Normal University;Jun2014, Vol. 48 Issue 3, p314
Let H be a Hilbert space. â„¬ (H) denotes the Banach space of all bounded linear operators of H into H. A class of analytic operator-valued functions in three-dimensional Hilbert space is introduced, â„‘ = {f (z) : f(z) = zI - .... is analytic on the unit disk | z | â‰¤1, where the...

- Initial states and decoherence of histories. Scherer, Artur; Soklakov, Andrei N. // Journal of Mathematical Physics;Apr2005, Vol. 46 Issue 4, p042108
We study decoherence properties of arbitrarily long histories constructed from a fixed projective partition of a finite dimensional Hilbert space. We show that decoherence of such histories for all initial states that are naturally induced by the projective partition implies decoherence for...

- INTERSECTIONS OF THE LEFT AND RIGHT ESSENTIAL SPECTRA OF $2\times 2$ UPPER TRIANGULAR OPERATOR MATRICES This topic is supported by the NSF of China.. YUAN LI; XIU-HONG SUN; HONG-KE DU // Bulletin of the London Mathematical Society;Nov2004, Vol. 36 Issue 6, p811
In this paper, perturbations of the left and right essential spectra of $2\times 2$ upper triangular operator matrix $M_C$ are studied, where $M_C= \left(\begin{smallmatrix} A & C 0 & B \end{smallmatrix}\right)$ is an operator acting on the Hilbert space ${\cal...

- Generalized Mahalanobis depth in the reproducing kernel Hilbert space. Hu, Yonggang; Wang, Yong; Wu, Yi; Li, Qiang; Hou, Chenping // Statistical Papers;Aug2011, Vol. 52 Issue 3, p511
In this paper, Mahalanobis depth (MHD) in the Reproducing Kernel Hilbert Space (RKHS) is proposed. First, we extend the notion of MHD to a generalized version, i.e., the generalized MHD (GHMD), to make it suitable for the small sample with singular covariance matrix. We prove that GMHD is...

- Semi—Fredholm Spectrum and Weyl's Theorem for Operator Matrices. Xiao Hong Cao; Mao Zheng Guo; Bin Meng // Acta Mathematica Sinica;Feb2006, Vol. 22 Issue 1, p169
When A âˆˆ B(H) and B âˆˆ B(K) are given, we denote by M C an operator acting on the Hilbert space H âŠ• K of the form $$ M_{C} = {\left( {\begin{array}{*{20}c} {A} & {C} \\ {0} & {B} \\ \end{array} } \right)} .$$ In this paper, first we give the necessary and sufficient condition...

- ON A J-POLAR DECOMPOSITION OF A BOUNDED OPERATOR AND MATRICES OF J-SYMMETRIC AND J-SKEW-SYMMETRIC OPERATORS. Zagorodnyuk, Sergey M. // Banach Journal of Mathematical Analysis;2010, Vol. 4 Issue 2, p11
In this paper we study a possibility of a decomposition of a bounded operator in a Hilbert space H as a product of a J-unitary and a J-self-adjoint operators, where J is a conjugation (an antilinear involution). This decomposition shows an inner structure of a bounded operator in a Hilbert...

- A NEW HALF-DISCRETE MULHOLLAND-TYPE INEQUALITY WITH PARAMETERS. BICHENG YANG // Annals of Functional Analysis;2012, Vol. 3 Issue 1, p142
By means of weight functions and Hadamard's inequality, a new half-discrete Mulholland-type inequality with a best constant factor is given. A best extension with parameters, some equivalent forms, the operator expressions as well as some particular cases are also considered.

- Series Expansion of a Function's Expectation Matrix at the Zero Interval Length Limit. Demıralp, Metin // AIP Conference Proceedings;9/6/2007, Vol. 936 Issue 1, p155
Expectation matrix of a function serves us to evaluate the expectation value of an algebraic multiplication-by-a-function type operator over a specified subspace of a given Hilbert space. It is also frequently called transition matrix due to quantum mechanical tradition. This work considers...