Linear Operators on a Vector Space

Abstract

We turn now to operators  on an LVS. To start with, we need a number of simple definitions. Most of these are obvious in the case of finite-dimensional vector spaces. But the case of infinite-dimensional spaces is nontrivial, and due care must be exercised. As always, I shall merely describe and list some relevant results in brief, without getting into technical details and proofs of assertions, or the formal mathematics. These details and formal proofs are, however, particularly important at least for some of the topics in this chapter. It is therefore advisable to supplement the discussion given here with more extended treatments to be found in standard texts on operator algebra and functional analysis (see, e.g., Bibliography).