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.
On minimizing the norm of linear maps in -classes.
On multilinear mappings of nuclear type.
The space of multilinear mappings of nuclear type (s;r1,...,rn) between Banach spaces is considered, some of its properties are described (including the relationship with tensor products) and its topological dual is characterized as a Banach space of absolutely summing mappings.
On norm closed ideals in
It is well known that the only proper non-trivial norm closed ideal in the algebra L(X) for (1 ≤ p < ∞) or X = c₀ is the ideal of compact operators. The next natural question is to describe all closed ideals of for 1 ≤ p,q < ∞, p ≠ q, or equivalently, the closed ideals in for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in , including one that has not been studied before. The proofs use various methods from Banach...
On operators factorizable through space
On operators induced by weakly 2-singular kernels
On operator-valued analytic functions with positive real part whose logarithm belongs to a class
On p-absolutely summing operators acting on Banach lattices
On proper boundary points of the spectrum and complemented eigenspaces.
On Quasi-Normality of Two-Sided Multiplication
2000 Mathematics Subject Classification: 47B47, 47B10, 47A30.In this note, we characterize quasi-normality of two-sided multiplication, restricted to a norm ideal and we extend this result, to an important class which contains all quasi-normal operators. Also we give some applications of this result.
On scalar-valued nonlinear absolutely summing mappings
We investigate cases ("coincidence situations") in which every scalar-valued continuous n-homogeneous polynomial (or every continuous n-linear mapping) is absolutely (p;q)-summing. We extend some well known coincidence situations and obtain several non-coincidence results, inspired by a linear technique due to Lindenstrauss and Pełczyński.
On some Banach ideals of operators
On some matrix Inequalities in Banach Spaces
On strongly -summing m-linear operators
We introduce and study a new concept of strongly -summing m-linear operators in the category of operator spaces. We give some characterizations of this notion such as the Pietsch domination theorem and we show that an m-linear operator is strongly -summing if and only if its adjoint is -summing.
On Tensor Product Characterization of Nuclear Spaces.
On the Clarkson-McCarthy Inequalities.
On the Cohen -nuclear sublinear operators.
On the compact non-nuclear operator problem.
On the differentiability of the norm in trace classes
On the dual of L(E, F).