scholarly journals Spectral properties and tensor products of quasi-*-A(n) operators

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1559-1565
Author(s):  
Junli Shen ◽  
Alatancang Chen
Keyword(s):  
Spectral Properties ◽  
Tensor Products ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

In this paper, we prove that the spectrum is continuous on the class of all quasi-*-A(n) operators. And we obtain a sufficient condition for a quasi-*-A(n) operator to be normal. Finally, we consider the tensor products of quasi-*-A(n) operators, giving a necessary and sufficient condition for T S to be a quasi-*-A(n) operator when T and S are both non-zero operators.

scholarly journals On Properties of ClassA(n)andn-Paranormal Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Xiaochun Li ◽  
Fugen Gao
Keyword(s):  
Positive Integer ◽  
Tensor Products ◽  
Unit Vector ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Direct Sum ◽  
Paranormal Operator ◽  
Necessary And Sufficient

Letnbe a positive integer, and an operatorT∈B(ℋ)is called a classA(n)operator ifT1+n2/1+n≥|T|2andn-paranormal operator ifT1+nx1/1+n≥||Tx||for every unit vectorx∈ℋ, which are common generalizations of classAand paranormal, respectively. In this paper, firstly we consider the tensor products for classA(n)operators, giving a necessary and sufficient condition forT⊗Sto be a classA(n)operator whenTandSare both non-zero operators; secondly we consider the properties forn-paranormal operators, showing that an-paranormal contraction is the direct sum of a unitary and aC.0completely non-unitary contraction.

scholarly journals Spectral Properties of Unitary Cayley Graphs of Finite Commutative Rings

10.37236/2390 ◽  
2012 ◽  
Vol 19 (4) ◽  
Author(s):  
Xiaogang Liu ◽  
Sanming Zhou
Keyword(s):  
Spectral Properties ◽  
Line Graph ◽  
Commutative Rings ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Absolute Value ◽  
Vertex Set ◽  
Finite Commutative Ring ◽  
Unitary Cayley Graph ◽  
Necessary And Sufficient

Let $R$ be a finite commutative ring. The unitary Cayley graph of $R$, denoted $G_R$, is the graph with vertex set $R$ and edge set $\left\{\{a,b\}:a,b\in R, a-b\in R^\times\right\}$, where $R^\times$ is the set of units of $R$. An $r$-regular graph is Ramanujan if the absolute value of every eigenvalue of it other than $\pm r$ is at most $2\sqrt{r-1}$. In this paper we give a necessary and sufficient condition for $G_R$ to be Ramanujan, and a necessary and sufficient condition for the complement of $G_R$ to be Ramanujan. We also determine the energy of the line graph of $G_R$, and compute the spectral moments of $G_R$ and its line graph.

Discreteness of spectrum for Schrödinger operators with δʹ-type conditions on infinite regular trees

2017 ◽  
Vol 147 (5) ◽  
pp. 1091-1117 ◽  
Author(s):  
Jia Zhao ◽  
Guoliang Shi ◽  
Jun Yan
Keyword(s):  
Schrödinger Operator ◽  
Spectral Properties ◽  
Schrödinger Operators ◽  
The Self ◽  
Schrodinger Operators ◽  
Sufficient Condition ◽  
Schrodinger Operator ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Form Approach

This paper deals with the spectral properties of self-adjoint Schrödinger operators with δʹ-type conditions on infinite regular trees. Firstly, we discuss the semi-boundedness and self-adjointness of this kind of Schrödinger operator. Secondly, by using the form approach, we give the necessary and sufficient condition that ensures that the spectra of the self-adjoint Schrödinger operators with δʹ-type conditions are discrete.

Tameness for the distribution of sums of Markov random variables

1997 ◽  
Vol 121 (1) ◽  
pp. 115-127 ◽  
Author(s):  
A. BISBAS ◽  
C. KARANIKAS ◽  
W. MORAN
Keyword(s):  
Maximal Ideal ◽  
Local Structure ◽  
Spectral Properties ◽  
Random Variables ◽  
Ideal Space ◽  
Probability Measures ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Markov Random ◽  
Necessary And Sufficient

This paper studies the spectral properties of a class of probability measures on the circle. The key aim is to describe the local structure of the maximal ideal space on the L-subspaces generated by the measures and hence the spectral properties of these measures. In particular we give a necessary and sufficient condition for such measures to belong to M0 (T).

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

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