Lower bounds for tau coefficients and operator norms using composite matrix norms

Bounds on norms of the adjoint matrix

An upper bound on operator norms of the adjoint matrix is presented, and special cases of the l 1 , l 2 and l 1 norms are investigated. The results are then used to obtain lower bounds on the smallest absolute value of an eigenvalue of a nonsingular matrix.

Norms, XOR Lemmas, and Lower Bounds for Polynomials and Protocols

This paper presents a unified and simple treatment of basic questions concerning two computational models: multiparty communication complexity and polynomials over GF(2). The key is the use of (known) norms on Boolean functions, which capture their proximity to each of these models (and are closely related to property testers of this proximity). The main contributions are new XOR lemmas. We sho...

Approximation norms and duality for communication complexity lower bounds

Correspondence between probabilistic norms and fuzzy norms

In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.

Estimating operator norms using covering nets

We present several polynomialand quasipolynomial-time approximation schemes for a large class of generalized operator norms. Special cases include the 2 → q norm of matrices for q > 2, the support function of the set of separable quantum states, finding the least noisy output of entanglement-breaking quantum channels, and approximating the injective tensor norm for a map between two Banach spac...