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Continuity of the spectrum on a class A(k)

김인현|전인호
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2013.03|한국수학논문집 (Korean Journal of Mathematics)|제21권 제1호|pp. 75-80|DOI http://dx.doi.org/10.11568/kjm.2013.21.1.75

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키워드

class A operatorsclass A(k) operatorsspectral continuities
주제분류수학

초록

Let T be a bounded linear operator on a complex Hilbertspace H . An operator T is called class A operator if ｜T2｜ ≥ ｜T｜2and is called class A(k) operator if (T*｜T｜2kT)1/k+1 ≥ ｜T｜2 for a pos-itive number k. In this paper, we show that σ is continuous whenrestricted to the set of class A(k) operators.

Abstract

Let T be a bounded linear operator on a complex Hilbertspace H . An operator T is called class A operator if ｜T2｜ ≥ ｜T｜2and is called class A(k) operator if (T*｜T｜2kT)1/k+1 ≥ ｜T｜2 for a pos-itive number k. In this paper, we show that σ is continuous whenrestricted to the set of class A(k) operators.

참고문헌 (16)

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