# Category:Banach Spaces

Jump to navigation
Jump to search

This category contains results about **Banach Spaces**.

Definitions specific to this category can be found in Definitions/Banach Spaces.

A **Banach space** is a normed vector space where every Cauchy sequence is convergent.

## Subcategories

This category has the following 14 subcategories, out of 14 total.

## Pages in category "Banach Spaces"

The following 45 pages are in this category, out of 45 total.

### A

- Absolute Net Convergence Equivalent to Absolute Convergence
- Absolutely Convergent Generalized Sum Converges
- Absolutely Convergent Generalized Sum Converges to Supremum
- Absolutely Convergent Series in Normed Vector Space is Convergent iff Space is Banach
- Absolutely Convergent Series is Convergent
- Analytic Function on Banach Space is Continuous

### B

### C

- Characterization of Complete Normed Quotient Vector Spaces
- Closed Subspace of Banach Space forms Banach Space
- Completion Theorem (Normed Vector Space)
- Complex Plane is Banach Space
- Condition for Equivalence of Norms that induce Banach Spaces
- Corollary of Generalized Sum with Countable Non-zero Summands
- C^k Function Space is Banach Space

### G

### I

### N

- Necessary and Sufficient Conditions for Continuous Linear Transformation Space to be Banach Space
- Net Convergence Equivalent to Absolute Convergence
- Neumann Series Theorem
- Neumann Series Theorem/Corollary 1
- Neumann Series Theorem/Corollary 2
- Non-Empty Bounded Above Subset of Banach Space with Archimedean Property has Supremum
- Norm Equivalence Preserves Completeness
- Normed Dual Space is Banach Space

### P

### S

- Set of Invertible Continuous Transformations is Open Subset of Continuous Linear Transformations in Supremum Operator Norm Topology
- Sobolev Space is Banach Space
- Space of Bounded Linear Transformations is Banach Space
- Space of Bounded Sequences with Supremum Norm forms Banach Space
- Space of Compact Linear Transformations is Banach Space
- Space of Continuous on Closed Interval Real-Valued Functions with Supremum Norm forms Banach Space
- Space of Continuously Differentiable on Closed Interval Real-Valued Functions with C^1 Norm is Banach Space
- Space of Zero-Limit Sequences with Supremum Norm forms Banach Space