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Fuglede-Putnam theorem for class A operators

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Mecheri S.

Colloquium Mathematicum

2015

tom 138

nr 2

183-191

Let A ∈ B(H) and B ∈ B(K). We say that A and B satisfy the Fuglede-Putnam theorem if AX = XB for some X ∈ B(K,H) implies A*X = XB*. Patel et al. (2006) showed that the Fuglede-Putnam theorem holds for class A(s,t) operators with s + t < 1 and they mentioned that the case s = t = 1 is still an open problem. In the present article we give a partial positive answer to this problem. We show that if A ∈ B(H) is a class A operator with reducing kernel and B* ∈ B(K) is a class 𝓨 operator, and AX = XB for some X ∈ B(K,H), then A*X = XB*.

Isolated points of spectrum of k-quasi-*-class A operators

100%

Mecheri S.

Studia Mathematica

2012

tom 208

nr 1

87-96

Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class, denoted 𝓚𝓠𝓐*, of operators satisfying $T^{*k}(|T²|-|T*|²)T^{k} ≥ 0$ where k is a natural number, and we prove basic structural properties of these operators. Using these results, we also show that if E is the Riesz idempotent for a non-zero isolated point μ of the spectrum of T ∈ 𝓚𝓠𝓐*, then E is self-adjoint and EH = ker(T-μ) = ker(T-μ)*. Some spectral properties are also presented.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Mecheri S.

1 2015

1 2012

Wyniki wyszukiwania

Fuglede-Putnam theorem for class A operators

Isolated points of spectrum of k-quasi-*-class A operators