Newbetuts

For Banach space there is a compact topological space so that the Banach space is isometrically isomorphic with a closed subspace of $C(X)$.

Quotient of a Banach space $X$ gets quotient topology under standard norm induced from $X$.

Why isometric isomorphic between Banach spaces means we can identify them?

Surjective bounded operator in Banach spaces without bounded right-inverse

$T$ is continuous $\iff \forall (x_1, x_2,..), x_i \in X, x_i \to^w x \implies T(x_i) \to^w T(x)$

Complementability of von Neumann algebras

Pointwise convergence in $c_0$ is not equivalent to weak convergence

Is there a direct proof that a compact unit ball implies automatic continuity?

Linear isometry between $c_0$ and $c$

If $X^\ast $ is separable $\Longrightarrow$ $S_{X^\ast}$ is also separable

Injectivity of the operator $(Ax)(t)=\int_0 ^1 k(s,t) x(s)ds$

Sequences are Cauchy depending on the norm?

Bochner Integral: Axioms

Show reflexive normed vector space is a Banach space

Operator norm on product space

If space of bounded operators L(V,W) is Banach, V nonzero, then W is Banach (note direction of implication)

New posts in banach-spaces

An approximate eigenvalue for $ T \in B(X) $.

Applications of the Hahn-Banach Theorems

Proving that a Banach space is separable if its dual is separable

Universal properties of mapping spaces in functional analysis

For Banach space there is a compact topological space so that the Banach space is isometrically isomorphic with a closed subspace of $C(X)$.

Quotient of a Banach space $X$ gets quotient topology under standard norm induced from $X$.

Why isometric isomorphic between Banach spaces means we can identify them?

Surjective bounded operator in Banach spaces without bounded right-inverse

$T$ is continuous $\iff \forall (x_1, x_2,..), x_i \in X, x_i \to^w x \implies T(x_i) \to^w T(x)$

Complementability of von Neumann algebras

Pointwise convergence in $c_0$ is not equivalent to weak convergence

Is there a direct proof that a compact unit ball implies automatic continuity?

Linear isometry between $c_0$ and $c$

If $X^\ast $ is separable $\Longrightarrow$ $S_{X^\ast}$ is also separable

Injectivity of the operator $(Ax)(t)=\int_0 ^1 k(s,t) x(s)ds$

Sequences are Cauchy depending on the norm?

Bochner Integral: Axioms

Show reflexive normed vector space is a Banach space

Operator norm on product space

If space of bounded operators L(V,W) is Banach, V nonzero, then W is Banach (note direction of implication)