BanachSpace concept

Description

A Banach space is a VectorSpace. A VectorSpace becomes a Banach space if it is equipped with a norm, denoted by ||x||.

Refinement of

Associated types

In addition to those defined by VectorSpace:
real_type: the result of the norm function

Notation

X A type that is a model of BanachSpace
v Object of type X

Definitions

Valid expressions

In addition to those defined by VectorSpace:
Name Expression Type requirements Return type
Norm v.norm() real_type

Expression semantics

Name Expression Precondition Semantics Postcondition
Norm v.norm() v.norm() ≥ 0

Complexity guarantees

Invariants

Models

Notes