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Muneo Chō

Bio: Muneo Chō is an academic researcher from Kanagawa University. The author has contributed to research in topics: Hilbert space & Operator theory. The author has an hindex of 9, co-authored 62 publications receiving 355 citations.


Papers
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Journal ArticleDOI
TL;DR: In this article, it was shown that if λ 0 is an isolated point of σ(T), then E is self-adjoint and EH =ker(T−λ 0)∗, then EH=ker( Tk).

38 citations

Journal ArticleDOI
TL;DR: In this article, an operator transform from class A to the class of hyponormal operators was given, and it was shown that every class A operator has SVEP and property β.
Abstract: In this paper, we shall give an operator transform \({\hat T}\) from class A to the class of hyponormal operators. Then we shall show that \(\sigma (T) = \sigma (\hat T)\) and \(\sigma_a (T) = \sigma_a (\hat T)\) in case T belongs to class A. Next, as an application of \({\hat T},\) we will show that every class A operator has SVEP and property (β).

37 citations

Journal ArticleDOI
TL;DR: In this article, the authors give an example of an ∞-hyponormal operator T whose Aluthge transform is not (1+√ + √)-hyponorm for any ǫ > 0 and show that the sequence of inter-aluthge transforms of T need not converge in weak operator topology.
Abstract: In this note we give an example of an ∞-hyponormal operator T whose Aluthge transform \( \widetilde T\) is not (1+ɛ)-hyponormal for any ɛ > 0 and show that the sequence \( \{ \widetilde T^{{(n)}} \} ^{\infty }_{{n = 1}} \) of interated Aluthge transforms of T need not converge in the weak operator topology, which solve two problems in [6].

34 citations


Cited by
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Journal ArticleDOI
01 Dec 1949-Nature
TL;DR: Wentzel and Jauch as discussed by the authors described the symmetrization of the energy momentum tensor according to the Belinfante Quantum Theory of Fields (BQF).
Abstract: To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

2,935 citations

Journal ArticleDOI

640 citations

Journal ArticleDOI
TL;DR: In this article, lecture notes for several courses on Functional Analysis at School of Mathematics of University of Leeds are presented. They are based on the notes of Dr. Matt Daws, Prof. Jonathan R. Partington and Dr. David Salinger used in the previous years.
Abstract: This is lecture notes for several courses on Functional Analysis at School of Mathematics of University of Leeds. They are based on the notes of Dr. Matt Daws, Prof. Jonathan R. Partington and Dr. David Salinger used in the previous years. Some sections are borrowed from the textbooks, which I used since being a student myself. However all misprints, omissions, and errors are only my responsibility. I am very grateful to Filipa Soares de Almeida, Eric Borgnet, Pasc Gavruta for pointing out some of them. Please let me know if you find more. The notes are available also for download in PDF. The suggested textbooks are [1,6,8,9]. The other nice books with many interesting problems are [3, 7]. Exercises with stars are not a part of mandatory material but are nevertheless worth to hear about. And they are not necessarily difficult, try to solve them! CONTENTS List of Figures 3 Notations and Assumptions 4 Integrability conditions 4 1. Motivating Example: Fourier Series 4 1.1. Fourier series: basic notions 4 1.2. The vibrating string 8 1.3. Historic: Joseph Fourier 10 2. Basics of Linear Spaces 11 2.1. Banach spaces (basic definitions only) 12 2.2. Hilbert spaces 14 2.3. Subspaces 16 2.4. Linear spans 19 3. Orthogonality 20 3.1. Orthogonal System in Hilbert Space 21 3.2. Bessel’s inequality 23 3.3. The Riesz–Fischer theorem 25 3.4. Construction of Orthonormal Sequences 26 3.5. Orthogonal complements 28 4. Fourier Analysis 29 Date: 16th October 2017. 1

512 citations

Journal ArticleDOI
TL;DR: This study considers linearly independent families of Hermitian matrices {A1, .
Abstract: Let A=(A1, . . ., Am) be an m-tuple of n × n Hermitian matrices. For $1 \le k \le n$, the $k${\rm th} joint numerical range of A is defined by $$W_k(A) = \{ ({\rm \tr}(X^*A_1X), \dots, {\rm \tr}(X^*A_mX) ): X \in {\bf C}^{n\times k}, X^*X = I_k \}.$$ We consider linearly independent families of Hermitian matrices {A1, . . . , Am} so that Wk(A) is convex. It is shown that m can reach the upper bound 2k(n-k)+1. A key idea in our study is relating the convexity of Wk(A) to the problem of constructing rank k orthogonal projections under linear constraints determined by A. The techniques are extended to study the convexity of other generalized numerical ranges and the corresponding matrix construction problems.

84 citations

Journal ArticleDOI
TL;DR: In this article, the concept of numerical range and maximal numerical range relative to a positive operator of a d-tuple of bounded linear operators on a Hilbert space was investigated, and it was shown that these sets are convex for d ≥ 2.

84 citations