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.

Namita Das P. G. Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, Orissa 751004, India Correspondence should be addressed to Namita Das, [email protected] Received 23 July 2009; Revised 7 September 2009; Accepted 14 October 2009 Recommended by Palle Jorgensen We have shown that if the Toeplitz operator Tφ on the Bergman space La D belongs to the Schatten class Sp, 1 ≤...

We generalize the theorems of Stein–Tomas and Strichartz about surface restrictions of Fourier transforms to systems of orthonormal functions with an optimal dependence on the number of functions. We deduce the corresponding Strichartz bounds for solutions to Schrödinger equations up to the endpoint, thereby solving an open problem of Frank, Lewin, Lieb and Seiringer. We also prove uniform Sobo...

A Helson matrix is an infinite $A = (a_{m,n})_{m,n\geq1}$ such that the entry $a_{m,n}$ depends only on product $mn$. We demonstrate orthogonal projection from Hilbert--Schmidt class $\mathcal{S}_2$ onto subspace of matrices does not extend to a bounded operator Schatten $\mathcal{S}_q$ for $1 \leq q \neq 2 < \infty$. In fact, we prove more general result showing large natural projections are u...

We investigate the norm of sums of independent vector-valued random variables in noncommutative Lp spaces. This allows us to obtain a uniform family of complete embeddings of the Schatten class S q in Sp(lmq ) with optimal order m ∼ n. Using these embeddings we show the surprising fact that the sharp type (cotype) index in the sense of operator spaces for Lp[0, 1] is min(p, p) (max(p, p)). Simi...

We study decoupling in quasi-Banach spaces. We show that decoupling is permissible in some quasi-Banach spaces (e.g., Lp and Lp/Hp when 0 < p < 1) but fails in other spaces such as the Schatten ideal Sp when 0 < p < 1. We also relate our ideas to a possible extension of the Grothendieck inequality.

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...