Factoring a Quadratic Operator as a Product of Two Positive Contractions
نویسندگان
چکیده
Let T be a quadratic operator on a complex Hilbert space H. We show that T can be written as a product of two positive contractions if and only if T is of the form aI ⊕ bI ⊕ ( aI P 0 bI ) on H1 ⊕H2 ⊕ (H3 ⊕H3) for some a, b ∈ [0, 1] and strictly positive operator P with ‖P‖ ≤ | √ a− √ b| √ (1− a)(1− b). Also, we give a necessary condition for a bounded linear operator T with operator matrix ( T1 T3 0 T2 ) on H ⊕K that can be written as a product of two positive contractions.
منابع مشابه
Positive Cone in $p$-Operator Projective Tensor Product of Fig`a-Talamanca-Herz Algebras
In this paper we define an order structure on the $p$-operator projective tensor product of Herz algebras and we show that the canonical isometric isomorphism between $A_p(Gtimes H)$ and $A_p(G)widehat{otimes}^p A_p(H)$ is an order isomorphism for amenable groups $G$ and $H$.
متن کاملA Note on Quadratic Maps for Hilbert Space Operators
In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...
متن کاملApproximating the Distributions of Singular Quadratic Expressions and their Ratios
Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...
متن کاملGeneralized multivalued $F$-contractions on non-complete metric spaces
In this paper, we explain a new generalized contractive condition for multivalued mappings and prove a fixed point theorem in metric spaces (not necessary complete) which extends some well-known results in the literature. Finally, as an application, we prove that a multivalued function satisfying a general linear functional inclusion admits a unique selection fulfilling the corresp...
متن کاملFactoring Integers Using the Web
This note provides background on the www-factoring project, which was started in the fall of 1995. Factoring a positive integer ri means finding two positive integers u and v such that the product of u and v equals ri, and such that both u a.nd v are greater than 1. Such u and v are called factors (or divisors) of ii, and n = u v is called a factorization of n. Positive integers that ca.n be fa...
متن کامل