Dilaton mass formulas in a hairy binary black hole model

In this note an analytic integration is obtained for the differential equation governing the scalar-field-dependent mass in a hairy binary black hole model, in the context of the Einstein–Maxwell–dilation theory, which gives a closed-form formula-level description of the mass function. We also identify a particular solution which attracts all solutions of the mass-governing equation exponentially rapidly in large-dilaton-field limit.

A Connes correspondence approach to the dilation theory

Product systems have been originally introduced to classify E0-semigroups on type I factors by Arveson. The idea of product systems is influenced the constructions of dilations of CP0-semigroups. In this paper, we will develop the dilation theory and the classification theory of E0-semigroups on a general von Neumann algebra in the view point of Connes correspondences. For this, we will provide a concept of product system whose components are Connes correspondences. There exists a one-to-one correspondence between a CP0-semigroup and a unit of a product system of Connes correspondences. The correspondence enables us to construct dilations and classify E0-semigroups by product systems of Connes correspondences up to cocycle equivalence.

Analytic Methods of Spectral Representations of Non- Selfadjoint (Non-Unitary) Operators

This book is concerned with model representations theory of linear non- selfadjoint and non-unitary operators, one of booming areas of functional analysis. This area owes its origin to fundamental works by M.S. Livˇsic on the theory of characteristic functions, deep studies of B.S.-Nagy and C. Foias on the dilation theory, and also to the Lax—Phillips scattering theory. A uni- form conceptual approach organically uniting all these research areas in the theory of non-selfadjoint and non-unitary operators is developed in this book. New analytic methods that allow solving some important problems from the theory of spectral representations in this area of analysis are also presented in this book. The book is aimed at the specialists working in this area of analysis and is accessible to senior math students of universities.

The Non-selfadjoint Approach to the Hao–Ng Isomorphism

In an earlier work, the authors proposed a non-selfadjoint approach to the Hao–Ng isomorphism problem for the full crossed product, depending on the validity of two conjectures stated in the broader context of crossed products for operator algebras. By work of Harris and Kim, we now know that these conjectures in the generality stated may not always be valid. In this paper we show that in the context of hyperrigid tensor algebras of $\mathrm{C}^*$-correspondences, each one of these conjectures is equivalent to the Hao–Ng problem. This is accomplished by studying the representation theory of non-selfadjoint crossed products of C$^*$-correspondence dynamical systems; in particular we show that there is an appropriate dilation theory. A large class of tensor algebras of $\mathrm{C}^*$-correspondences, including all regular ones, are shown to be hyperrigid. Using Hamana’s injective envelope theory, we extend earlier results from the discrete group case to arbitrary locally compact groups; this includes a resolution of the Hao–Ng isomorphism for the reduced crossed product and all hyperrigid $\mathrm{C}^*$-correspondences. A culmination of these results is the resolution of the Hao–Ng isomorphism problem for the full crossed product and all row-finite graph correspondences; this extends a recent result of Bedos, Kaliszewski, Quigg, and Spielberg.

Factorization of an adjontable Markov operator

In this work, we propose a method to investigate the factorization property of a adjontable Markov operator between two algebraic probability spaces without using the dilation theory. Assuming the existence of an anti-unitary operator on Hilbert space related to Stinespring representations of our Markov operator, which satisfy some particular modular relations, we prove that it admits a factorization. The method is tested on the two typologies of maps which we know admits a factorization, the Markov operators between commutative probability spaces and adjontable homomorphism. Subsequently, we apply these methods to particular adjontable Markov operator between matrix algebra which fixes the diagonal.