Every $L\sb{p}$ operator is an $L\sb{2}$ operator

Almost every graph is divergent under the biclique operator

A biclique of a graph G is a maximal induced complete bipartite subgraph of G. The biclique graph of G denoted by KB(G), is the intersection graph of all the bicliques of G. The biclique graph can be thought as an operator between the class of all graphs. The iterated biclique graph of G denoted by KBk(G), is the graph obtained by applying the biclique operator k successive times to G. The asso...

What Is an Operator Space?

These are notes for a lecture delivered on 12 May, 2008, in a graduate course on operator algebras in Berkeley. The intent was to give a brief introduction to the basic ideas of operator space theory. The notes were hastily written and have not been carefully checked for accuracy or political correctness. 1. An overview of operator spaces We learn early on that every Banach space S is isometric...

An Operator Extension of Bohr's inequality

AN EFFICIENT CROSSOVER OPERATOR FOR TRAVELING SALESMAN PROBLEM

Crossover operator plays a crucial role in the efficiency of genetic algorithm (GA). Several crossover operators have been proposed for solving the travelling salesman problem (TSP) in the literature. These operators have paid less attention to the characteristics of the traveling salesman problem, and majority of these operators can only generate feasible solutions. In this paper, a crossover ...

Every maximally monotone operator of Fitzpatrick-Phelps type is actually of dense type

We show that every maximally monotone operator of Fitzpatrick-Phelps type defined on a real Banach space must be of dense type. This provides an affirmative answer to a question posed by Stephen Simons in 2001 and implies that various important notions of monotonicity coincide. 2010 Mathematics Subject Classification: Primary 47H05; Secondary 46B10, 47N10, 90C25