A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.

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**1**answer

### Closure of tensor product /tensor product semigroup

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### Nonlinear maps in Riesz Thorin theorem

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**0**answers

### Why ker(1) is a semi M-ideal in $\ell_1$?

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**1**answer

### If $E\oplus_\phi E \cong E\oplus_\psi E,$ does it imply that $\phi= \psi$?

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**1**answer

### Does there exists an extreme point $(a_1^*,…,a_n^*)$ of $B_{\mu^*}$ such that $a_i^*\neq 0$ for all $1\leq i\leq n$ and $\sum_{I=1}^n a_i^*a_i=1?$

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**1**answer

### Do functions exist and are they dense? Or does it depend on the basis?

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**0**answers

### The dual relationships between strictly singular operators and strictly cosingular operators

**4**

**1**answer

### Approximation property counterexamples? (Also: relation to tensor products)

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**1**answer

### A formula for vector valued measurable functions

**1**

**1**answer

### Compactness of operators and norming sets

**1**

**1**answer

### Infinitely many independent functions that are only frequency localized?

**0**

**1**answer

### Central limit theorem in Banach space in scheme of series

**3**

**1**answer

### Does Bishop-Phelps Theorem hold for extreme points (slightly different version)?

**3**

**3**answers

### Preannihilators of subspaces of separable duals

**3**

**1**answer

### Does separability of the strong operator topology imply separability of the underlying space?

**7**

**2**answers

### If the cardinality of $B(X)$, the space of operators on $X$, is continuum, must $X$ be separable?

**3**

**1**answer

### Norming functionals for vectors in intersections

**2**

**1**answer

### Relation between the weak star topology and hereditary Lindelöfness

**8**

**1**answer

### Lipschitz right inverses of Banach space quotients

**4**

**2**answers

### pointwise convergence to the identity

**3**

**0**answers

### point-wise approximation of the identity in hereditary Lindelof spaces

**7**

**1**answer

### Subspaces isomorphic with quotients

**4**

**0**answers

### Is this property an isomorphic characterization of $\ell_1(\Gamma)$?

**10**

**1**answer

### Are all compact subsets of Banach spaces small in a measure-theoretic sense?

**1**

**0**answers

### Status of an open problem in isometric aspect of Banach space theory

**1**

**3**answers

### $c_0$ is not isometrically isomorphic to $c$

**1**

**1**answer

### A particular separation example

**4**

**1**answer

### The largest topological copy of a Hilbert space contained in $\ell^1$

**9**

**1**answer

### Comparing two $\sigma$-algebras on $B(\ell^1)$

**5**

**3**answers

### Point-wise limit of finite valued functions

**4**

**1**answer

### Dual of the space of all bounded holomorphic functions

**3**

**1**answer

### Separable Lindelöf locally convex spaces that are not second-countable

**2**

**1**answer

### A particular example of topological vector spaces

**7**

**2**answers

### Is the strong operator topology metrizable?

**7**

**0**answers

### Status of two Banach space theory open problems posted by Pełczyński

**0**

**0**answers

### Topologies corresponding to norm, SOT and WOT under duality

**6**

**1**answer

### Embedding the $\ 2^n+1$-point metric 1-space

**5**

**1**answer

### Is each compact metric space a subset of a compact absolute 1-Lipschitz retract?

**3**

**0**answers

### Is the Banach space $C(K)$ a $1$-Lipschitz comp-extensor?

**7**

**1**answer

### What is the smallest Lipschitz constant of a Lipschitz retraction of $\ell_\infty([0,1])$ onto $C[0,1]$?

**1**

**2**answers

### For what points in $\mathbb R^2$ does the triangular condition fail for a 1/2-metric?

**8**

**1**answer

### Why $S$ cannot be homeomorphic to the $1$-sphere of $\ell^2$?

**7**

**0**answers

### Equivalent strictly convex norms in spaces of small density

**2**

**1**answer

### A Question about an irreducible ultra-power II,

**1**

**0**answers

### Weak$^*$ topology on Bochner $L^p$-spaces

**8**

**1**answer

### Two questions about basic sequences

**0**

**0**answers

### Weak convergence can imply strong convergence [duplicate]

**2**

**1**answer

### Duality of Bochner $L^{\infty}$ space

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**0**answers

### Projection semigroup of an isolated eigenvalue

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**0**answers