## Introduction to Functional Analysis, Banach Spaces, and Differential Calculus |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Common terms and phrases

addition algebraic Analysis applied ball Banach space bilinear bounded called cartesian product Chapter classical closed complete conclude condition connected consequence consider constant contained converges Corollary corresponds define DEFINITION denoted derivative Df(x differ differentiability of f differentiable of order differential calculus direct sum element equality equation equivalent Example EXERCISE Let exists F be normed f is continuous f is differentiable fact finite dimensional Fixing follows function function f given Hence holds homeomorphism hypothesis immediate implies inequality infinite integral inverse isomorphism Lagrange Lemma Let E limit llull loll mapping mean value theorem metric space natural nonempty open set normed space OBSERVATION obtain once differentiable partially differentiable Proof PROPOSITION Let prove respectively result satisfies scalar sense space E sufficient suppose theorem Theory tion topology unique University variable vector space vector subspace xoll