A survey of some recent inequalities for the norm and numerical radius of operators in Hilbert spaces.
A theorem of Rolewicz's type for measurable evolution families in Banach spaces.
A trace inequality for functions of triangular Hilbert-Schmidt operators
Absolutely--summing operators in -spaces I
Absolutely--summing operators in -spaces II
AMD-numbers, compactness, strict singularity and the essential spectrum of operators.
An Inequality Involving a Hermitian Operator and its Square in a Normed Space
An interpolation theorem with -weighted spaces
An Operator Inequality.
Another version of Anderson's inequality in the ideal of all compact operators.
Banach ideals on Hilbert spaces
Bessel and Grüss type inequalities in inner product modules over Banach -algebras.
Best approximation in spaces of bounded linear operators [Book]
Best constants for some operators associated with the Fourier and Hilbert transforms
We determine the norm in , 1 < p < ∞, of the operator , where and are respectively the cosine and sine Fourier transforms on the positive real axis, and I is the identity operator. This solves a problem posed in 1984 by M. S. Birman [Bir] which originated in scattering theory for unbounded obstacles in the plane. We also obtain the -norms of the operators aI + bH, where H is the Hilbert transform (conjugate function operator) on the circle or real line, for arbitrary real a,b. Best...
Bicontractive projections in sequence spaces and a few related kinds of maps
Bilinear Mappings and Trace Class Ideals.
Boundedness for multilinear Marcinkiewicz operators on certain Hardy spaces.
Boundedness of sublinear operators on the homogeneous Herz spaces.
Some boundedness results are established for sublinear operators on the homogeneous Herz spaces. As applications, some new theorems about the boundedness on homogeneous Herz spaces for commutators of singular integral operators are obtained.
Boundedness properties of resolvents and semigroups of operators
Let T: H → H be an operator in the complex Hilbert space H. Suppose that T is square bounded in average in the sense that there exists a constant M(T) with the property that, for all natural numbers n and for all x ∈ H, the inequality is satisfied. Also suppose that the adjoint T* of the operator T is square bounded in average with constant M(T*). Then the operator T is power bounded in the sense that is finite. In fact the following inequality is valid for all n ∈ ℕ: ∥Tn∥ ≤ e M(T)M(T*). Suppose...
Brushlet characterization of the Hardy space H1(R) and the space BMO.
A typical wavelet system constitutes an unconditional basis for various function spaces -Lebesgue, Besov, Triebel-Lizorkin, Hardy, BMO. One of the main reasons is the frequency localization of an element from such a basis. In this paper we study a wavelet-type system, called a brushlet system. In [3] it was noticed that brushlets constitute unconditional bases for classical function spaces such as the Triebel-Lizorkin and Besov spaces. In this paper we study brushlet expansions of functions in the...