List questions from banach-algebras

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Looking for an easy lightning introduction to Hilbert spaces and Banach spaces

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Prove the approximate identity from the unitization

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A question about Banach algebras: showing that $\operatorname{Sp}a \subset D_o \cup D_1$

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Example of a singular element which is not a topological divisor of zero

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List Question

A Banach algebra that cannot be represented on a Hilbert space

Looking for an easy lightning introduction to Hilbert spaces and Banach spaces

Resolution of Identity

Prove the approximate identity from the unitization

The spectrum of a commutative unital Banach algbra having linearly dense idempotents is totally disconnected

Commutative unital Banach algebra with nilpotent elements

Commutative Noetherian Banach algebra.

A question about Banach algebras: showing that $\operatorname{Sp}a \subset D_o \cup D_1$

Roots in Banach algebras.

Uniqueness of the involution on a $C^*$-algebra

Invertibility of elements in a Banach algebra

Character space of $L^{1} (\mathbb Z)$

Example of a singular element which is not a topological divisor of zero

Definite positive measure and GNS representation

Gelfand transform is an isometry

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