Alpha-Beta Log-Determinant Divergences Between Positive Definite Trace Class Operators

2019 ◽  
Vol 2 (2) ◽  
pp. 101-176 ◽  
Author(s):  
Hà Quang Minh
Keyword(s):  
Trace Class ◽  
Positive Definite ◽  
Trace Class Operators ◽  
Alpha Beta

scholarly journals Some inequalities for trace class operators via a Kato’s result

2017 ◽  
Vol 11 (01) ◽  
pp. 1850004
Author(s):  
S. S. Dragomir
Keyword(s):  
Hilbert Space ◽  
Power Series ◽  
Trace Class ◽  
Complex Hilbert Space ◽  
Normal Operators ◽  
Trace Class Operators ◽  
Kato’S Inequality ◽  
New Inequalities

By the use of the celebrated Kato’s inequality, we obtain in this paper some new inequalities for trace class operators on a complex Hilbert space [Formula: see text] Natural applications for functions defined by power series of normal operators are given as well.

scholarly journals Fisher information for inverse problems and trace class operators

2012 ◽  
Vol 53 (12) ◽  
pp. 123503 ◽  
Author(s):  
S. Nordebo ◽  
M. Gustafsson ◽  
A. Khrennikov ◽  
B. Nilsson ◽  
J. Toft
Keyword(s):  
Inverse Problems ◽  
Fisher Information ◽  
Trace Class ◽  
Trace Class Operators

Trace Class Elements and Cross-Sections in Kac-Moody Groups

1998 ◽  
Vol 50 (5) ◽  
pp. 972-1006 ◽  
Author(s):  
Gerd Brüchert
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Trace Class ◽  
Irreducible Representations ◽  
Functional Identity ◽  
Trace Class Operators ◽  
Regular Classes

AbstractLet G be an affine Kac-Moody group, π0, … ,πr, πδ its fundamental irreducible representations and χ0, … , χr, χδ their characters. We determine the set of all group elements x such that all πi(x) act as trace class operators, i.e., such that χi(x) exists, then prove that the χ i are class functions. Thus, χ := (χ0, … , χr, χδ) factors to an adjoint quotient χ for G. In a second part, following Steinberg, we define a cross-section C for the potential regular classes in G. We prove that the restriction χ|C behaves well algebraically. Moreover, we obtain an action of C ℂ✗ on C, which leads to a functional identity for χ|C which shows that χ|C is quasi-homogeneous.

Range Inclusion for Multilinear Mappings: Applications

1985 ◽  
Vol 28 (3) ◽  
pp. 317-320
Author(s):  
C. K. Fong
Keyword(s):  
Hilbert Space ◽  
Finite Rank ◽  
Trace Class ◽  
Inner Derivation ◽  
Finite Rank Operators ◽  
Multilinear Mappings ◽  
Trace Class Operators ◽  
The Ideal

AbstractThe result of S. Grabiner [5] on range inclusion is applied for establishing the following two theorems: 1. For A, B ∊ L(H), two operators on the Hilbert space H, we have DBC0(H) ⊆ DAL(H) if and only if DBC1(H) ⊆ DAL(H), where DA is the inner derivation which sends S ∊ L(H) to AS - SA, C1(H) is the ideal of trace class operators and C0(H) is the ideal of finite rank operators. 2. (Due to Fialkow [3]) For A, B ∊ L(H), we write T(A, B) for the map on L(H) sending S to AS - SB. Then the range of T(A, B)is the whole L(H) if it includes all finite rank operators L(H).

scholarly journals Compactness properties for trace-class operators and applications to quantum mechanics

2008 ◽  
Vol 155 (1) ◽  
pp. 43-66 ◽  
Author(s):  
J. Dolbeault ◽  
P. Felmer ◽  
J. Mayorga-Zambrano
Keyword(s):  
Quantum Mechanics ◽  
Trace Class ◽  
Trace Class Operators

scholarly journals Schatten's theorems on functionally defined Schur algebras

2005 ◽  
Vol 2005 (14) ◽  
pp. 2175-2193 ◽  
Author(s):  
Pachara Chaisuriya ◽  
Sing-Cheong Ong
Keyword(s):  
Hilbert Space ◽  
Banach Algebra ◽  
Bounded Operator ◽  
Trace Class ◽  
Compact Operators ◽  
Bounded Operators ◽  
Schur Algebras ◽  
Schur Product ◽  
Product Operation ◽  
Trace Class Operators

For each triple of positive numbersp,q,r≥1and each commutativeC*-algebraℬwith identity1and the sets(ℬ)of states onℬ, the set𝒮r(ℬ)of all matricesA=[ajk]overℬsuch thatϕ[A[r]]:=[ϕ(|ajk|r)]defines a bounded operator fromℓptoℓqfor allϕ∈s(ℬ)is shown to be a Banach algebra under the Schur product operation, and the norm‖A‖=‖|A|‖p,q,r=sup{‖ϕ[A[r]]‖1/r:ϕ∈s(ℬ)}. Schatten's theorems about the dual of the compact operators, the trace-class operators, and the decomposition of the dual of the algebra of all bounded operators on a Hilbert space are extended to the𝒮r(ℬ)setting.

scholarly journals Contractions of Product Density Operators of Systems of Identical Fermions and Bosons

2010 ◽  
Vol 2010 ◽  
pp. 1-26 ◽  
Author(s):  
Wiktor Radzki
Keyword(s):  
Thermodynamic Limit ◽  
Single Particle ◽  
Trace Class ◽  
Asymptotic Equivalence ◽  
Product Density ◽  
Expectation Values ◽  
Symmetric Products ◽  
Density Operators ◽  
Trace Class Operators ◽  
Explicit Formulae

Recurrence and explicit formulae for contractions (partial traces) of antisymmetric and symmetric products of identical trace class operators are derived. Contractions of product density operators of systems of identical fermions and bosons are proved to be asymptotically equivalent to, respectively, antisymmetric and symmetric products of density operators of a single particle, multiplied by a normalization integer. The asymptotic equivalence relation is defined in terms of the thermodynamic limit of expectation values of observables in the states represented by given density operators. For some weaker relation of asymptotic equivalence, concerning the thermodynamic limit of expectation values of product observables, normalized antisymmetric and symmetric products of density operators of a single particle are shown to be equivalent to tensor products of density operators of a single particle.

scholarly journals THE ALPHA-BETA-SYMMETRIC DIVERGENCE AND THEIR POSITIVE DEFINITE KERNELS

2018 ◽  
Vol 53 (1) ◽  
pp. 75-100
Author(s):  
Mactar Ndaw ◽  
◽  
Macoumba Ndour ◽  
Papa Ngom ◽  
◽  
...  
Keyword(s):  
Positive Definite ◽  
Positive Definite Kernels ◽  
Alpha Beta
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