Gâteaux derivative and orthogonality in -classes.
Relation between best approximant and orthogonality in -classes.
Fuglede-Putnam theorem for class A operators
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 =...
Isolated points of spectrum of k-quasi-*-class A operators
Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class, denoted *, of operators satisfying 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 ∈ *, then E is self-adjoint and EH = ker(T-μ) = ker(T-μ)*. Some spectral properties are also presented.
Commutants and derivation ranges
In this paper we obtain some results concerning the set , where is the closure in the norm topology of the range of the inner derivation defined by Here stands for a Hilbert space and we prove that every compact operator in is quasinilpotent if is dominant, where is the closure of the range of in the weak topology.
Some versions of Anderson's and Maher's inequalities. I.
Some versions of Anderson's and Maher's inequalities. II.
Gâteaux derivative and orthogonality in -classes.
Generalized derivations and -algebras.
Generalized derivations and -algebras: comments and some open problems.
Another version of Anderson's inequality in the ideal of all compact operators.
On the normality of operators.
-symmetric operators: comments and some open problems.
On Minimizing ||S−(AX−XB)||Pp
In this paper, we minimize the map Fp (X)= ||S−(AX−XB)||Pp , where the pair (A, B) has the property (F P )Cp , S ∈ Cp , X varies such that AX − XB ∈ Cp and Cp denotes the von Neumann-Schatten class.
Some variants of Anderson's inequality in -classes.
Generalized derivation modulo the ideal of all compact operators.
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