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.
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.
Page 1