# Category:Functional Analysis

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This category contains results about **Functional Analysis**.

Definitions specific to this category can be found in Definitions/Functional Analysis.

**Functional analysis** is a branch of analysis, which studies vector spaces endowed a structure such as inner product, norm or topology.

It can be understood as the study of analysis, including calculus, both differential and integral, to Banach spaces.

## Subcategories

This category has the following 42 subcategories, out of 42 total.

### B

- Banach Fixed-Point Theorem (6 P)
- Banach-Alaoglu Theorem (10 P)
- Banach-Steinhaus Theorem (10 P)

### C

- Continuous Operators (1 P)

### D

- Distributional Partial Derivatives (empty)

### E

### F

- Fredholm Operators (3 P)

### H

- Hahn-Banach Separation Theorem (16 P)
- Hahn-Banach Theorem (9 P)

### I

### L

- Lipschitz Norm (empty)
- Lipschitz Spaces (empty)

### N

### P

- P-Norms (8 P)
- P-Sequence Spaces (1 P)

### R

- Riesz's Lemma (3 P)

### S

### T

### W

## Pages in category "Functional Analysis"

The following 49 pages are in this category, out of 49 total.

### B

### C

### D

### F

### H

### I

### L

### P

### R

- Resolvent Mapping Converges to 0 at Infinity
- Resolvent Mapping is Analytic/Bounded Linear Operator
- Resolvent Mapping is Analytic/Bounded Linear Operator/Proof 1
- Resolvent Mapping is Analytic/Bounded Linear Operator/Proof 2
- Reverse Hölder's Inequality for Sums
- Riesz's Lemma
- Riesz-Kakutani Representation Theorem
- Ruelle-Perron-Frobenius Theorem

### S

- Space of Bounded Sequences with Pointwise Addition and Pointwise Scalar Multiplication on Ring of Sequences forms Vector Space
- Space of Bounded Sequences with Supremum Norm forms Banach Space
- Space of Continuous on Closed Interval Real-Valued Functions with Pointwise Addition and Pointwise Scalar Multiplication forms Vector 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 Pointwise Addition and Pointwise Scalar Multiplication forms Vector Space
- Space of Lipschitz Functions is Banach Space/Shift of Finite Type
- Space of Piecewise Linear Functions on Closed Interval is Dense in Space of Continuous Functions on Closed Interval
- Space of Somewhere Differentiable Continuous Functions on Closed Interval is Meager in Space of Continuous Functions on Closed Interval
- Space of Somewhere Differentiable Continuous Functions on Closed Interval is Meager in Space of Continuous Functions on Closed Interval/Corollary