Algebry operatorów i ich zastosowania w fizyce

In the theory of operator spaces we consider Banach spaces endowed with a particular embedding into B(H) -- the algebra of bounded operators on a Hilbert space. This gives us a sequence of norms on spaces of matrices with entries in a given Banach space. There exist the largest and the smallest sequences of such norms corresponding to some embedding into B(H). If the sequence of norms obtained for a Banach space X is the largest one then we call it a maximal operator space. We will show many examples of subspaces of maximal operator spaces which are not maximal themselves, using mostly tools from classical theory of Banach spaces. As a by-product we will answer the question of Vern Paulsen concerning amalgamated direct sums.