Category:Banach Spaces
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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