2 Definitions and main results 3 2.1 Notations and definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Graph norms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Schatten-von Neumann classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Hölder and weakly Hölder graphs . . . . . . . . . . . . ....

In this paper we analyse optimality of the stable fixed point of the double bracket equations. We introduce different types of optimality and prove local and global optimality results with respect to the Schatten p-norms.

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...

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.

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 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.