Spectrum of Class wF(p,r,q) Operators

Integr. equ. oper. theory

2007

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Inspired by the problem of powers of hyponormal operators, this paper is to discuss the structure on powers of p-hyponormal and log-hyponormal operators. The structure on powers of operators consists of same-side structure and different-side structure. The same-side structure means relations between T * n+m T n+m and T * n T n (or T n T * n and T n+m T * n+m ), and the different-side structure means relations between T * m T m and T n T * n where m, n are positive integers and T is a bounded linear operator on a Hilbert space. Thus, the original problem of powers of hyponormal operators belongs to differentside structure on powers of hyponormal operators. The structure on powers of p-hyponormal operators for p > 0 is emphasized. Also, some applications are obtained. Mathematics Subject Classification (2000). 47B20, 47A63.

Section: Theorem 11 ([2]) If N Is a Positive Integer And T Ismentioning

confidence: 55%

“…This has been generalized to more wide classes of operators [3,28]. Let T be a log-hyponormal operator and n be a positive integer.…”

Section: Applicationsmentioning

confidence: 99%

Structure on Powers of p-Hyponormal and log-Hyponormal Operators

Integr. equ. oper. theory

2007

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“…[29]). Recently, some researchers showed that, for some nonnormal operators T , the nonzero points of its point spectrum and joint point spectrum are identical, the nonzero points of its approximate point spectrum and joint approximate point spectrum are identical (cf.…”

Section: Spectrum Of Class A(n)mentioning

confidence: 99%

“…Recently, some researchers showed that, for some nonnormal operators T , the nonzero points of its point spectrum and joint point spectrum are identical, the nonzero points of its approximate point spectrum and joint approximate point spectrum are identical (cf. [3,7,25,29]). In this section, we shall extend this result to class A(n) and show that the spectral mapping theorem on Weyl spectrum holds for class A(n) by using a different method.…”

Section: Spectrum Of Class A(n)mentioning

confidence: 99%

Weyl Spectrum of Class A(n) and n-Paranormal Operators

Integr. equ. oper. theory

2008

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Let n be a positive integer, an operator T belongs to class A(n) if |T 1+n | 2/(1+n) ≥ |T | 2 , which is a generalization of class A and a subclass of n-paranormal operators, i.e., T 1+n x 1/(1+n) ≥ T x for unit vector x. It is showed that if T is a class A(n) or n-paranormal operator, then the spectral mapping theorem on Weyl spectrum of T holds. If T belongs to class A(n), then the nonzero points of its point spectrum and joint point spectrum are identical, the nonzero points of its approximate point spectrum and joint approximate point spectrum are identical.

“…It's well known that Furuta inequality has many applications. See [3], [7], [11] and [23]. It has been generalized to grand Furuta inequality and it extended the Ando-Hiai log-majorization theory [8,15,22].…”

Section: Theorem 11 ([4]) Ifmentioning

confidence: 99%

Complete form of Furuta inequality

2008

Proc. Amer. Math. Soc.

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Abstract. Let A and B be bounded linear operators on a Hilbert space satisfying A ≥ B ≥ 0. The well-known Furuta inequality is given as follows: Let. In order to give a self-contained proof of it, Furuta (1989) p+r p+r . This paper aims to show a sharpening of Furuta (1989)s+r p+r . We call it the complete form of Furuta inequality because the case p 0 = 1 of it implies the essential part (p > 1) of Furuta inequality for 1+r s+r ∈ (0, 1] by the famous Löwner-Heinz inequality. Afterwards, the optimality of the outer exponent of the complete form is considered. Lastly, we give some applications of the complete form to Aluthge transformation.