The goal of this paper is to study tractable iteration mechanisms for bags. The presence of duplicates in bags prevents iteration mechanisms developed in the context of sets to be directly applied to bags without losing tractability. We study two constructs for controlling tractability of iteration over bags. The deeationary xpoint construct keeps removing elements from a bag until a xpoint is ...

We show that the action of Kauffman bracket skein algebra a surface Σ on module handlebody bounded by is faithful if and only quantum parameter not root 1.

Combining graph theory and linear algebra, we study SAT problems of low “linear algebra complexity”, considering formulas with bounded hermitian rank. We show polynomial time SAT decision of the class of formulas with hermitian rank at most one, applying methods from hypergraph transversal theory. Applications to heuristics for SAT algorithms and to the structure of minimally unsatisfiable clau...

A Boolean algebra has the Nikodym property if every pointwise bounded sequence of finitely additive measures on is uniformly bounded. Assuming Diamond Principle ◇, we will construct an example a minimally generated with property. The Stone space such must necessarily be Efimov space. converse is, however, not true—again under ◇ provide whose but which does have results interesting measure-theor...

We study the growth of polynomials on semialgebraic sets. For this purpose we associate a graded algebra to the set, and address all kinds of questions about finite generation. We show that for a certain class of sets, the algebra is finitely generated. This implies that the total degree of a polynomial determines its growth on the set, at least modulo bounded polynomials. We however also provi...

What follows is propaganda for the study of a particular commutative Banach algebra, A one not inappropriate to a conference which emphasises automatic continuity. In fact A is that subalgebra of the measure algebra, .i\J(T), of all regular bounded Borel measures on the circle under the total variation norm and convolution multiplication, which is characterised by the automatic continuity of me...

We prove that the normal cohomology groups H w(M, K(H)) of a von Neumann algebra M with coefficients in the algebra of compact operators are zero if M is atomic of type Ifin. In addition, the completely bounded normal cohomology groups H wcb(B(H), K(H)) are shown to be 0 as well.

Let {Dn} be a sequence of bounded invertible operators on Hilbert space H. It is shown that the collection of operators T for which the norm-limit limDnTD n exists is an algebra. Furthermore, some sufficient conditions on this sequence are established for the corresponding algebra to have a nontrivial invariant subspace. By considering specific sequences of operators several invariant subspace ...

Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new s...

For each triple of positive numbers p,q,r ≥ 1 and each commutative C-algebra with identity 1 and the set s( ) of states on , the set r ( ) of all matrices A = [ajk] over such that φ[A [r] ] := [φ(|ajk|r )] defines a bounded operator from p to q for all φ ∈ s( ) is shown to be a Banach algebra under the Schur product operation, and the norm ||A|| = |||A|||p,q,r = sup{||φ[A[r] ]||1/r : φ ∈ s( )}....