Let Sp be the von Neumann-Schatten ideal of compact operators in a separable Hilbert space. In the paper, upper and lower bounds for the regularized determinants of operators from Sp are established.

In ‎the present ‎paper, ‎we ‎introduce the ‎two-wavelet ‎localization ‎operator ‎for ‎the square ‎integrable ‎representation ‎of a‎ ‎homogeneous space‎ with respect to a relatively invariant measure. ‎We show that it is a bounded linear operator. We investigate ‎some ‎properties ‎of the ‎two-wavelet ‎localization ‎operator ‎and ‎show ‎that ‎it ‎is a‎ ‎compact ‎operator ‎and is ‎contained ‎in‎ a...

Abstract. There are well-known relationships between compressed sensing and the geometry of the finite-dimensional lp spaces. A result of Kashin and Temlyakov [20] can be described as a characterization of the stability of the recovery of sparse vectors via l1minimization in terms of the Gelfand widths of certain identity mappings between finitedimensional l1 and l2 spaces, whereas a more recen...

We prove that non-commutative martingale transforms are of weak type (1, 1). More precisely, there is an absolute constant C such that if M is a semi-finite von Neumann algebra and (Mn)n=1 is an increasing filtration of von Neumann subalgebras of M then for any non-commutative martingale x = (xn) ∞ n=1 in L 1(M), adapted to (Mn)n=1, and any sequence of signs (εn) ∞ n=1, ∥∥∥∥ε1x1 + N ∑ n=2 εn(xn...

For positive Toeplitz operators on Bergman spaces of the unit ball, we determine exactly when membership in the Schatten classes Sp can be characterized in terms of the Berezin transform.

We consider Schatten ́s equation in connection with a Banach algebra and Banach modules. From this connection we infer a new proof of the fact that the second action of a bounded derivation is also a bounded derivation.

in this paper, we considered composition operators on weighted hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a hilbert-schmidt characterization and characterizes the membership in schatten-class for these operators. also, closed range composition operators  are investigated.