## Functiones et Approximatio Commentarii Mathematici

- Funct. Approx. Comment. Math.
- Volume 53, Number 2 (2015), 189-192.

### All maximal commutative subalgebras occur in $L(X)$ uncountably many times

#### Abstract

We show that for every Banach space $X, \dim X>1$, every maximal commutative subalgebra of $L(X)$ has uncountably many copies between maximal commutative subalgebras of $L(X)$. Answering to a question of Aleksander Pe{\l}czy\'nski, we show also that for an arbitrary infinite dimensional Banach space $X$ there are at least countably many multiplications making of $X$ a commutative unital Banach algebra.

#### Article information

**Source**

Funct. Approx. Comment. Math., Volume 53, Number 2 (2015), 189-192.

**Dates**

First available in Project Euclid: 17 December 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.facm/1450389051

**Digital Object Identifier**

doi:10.7169/facm/2015.53.2.2

**Mathematical Reviews number (MathSciNet)**

MR3435796

**Zentralblatt MATH identifier**

1093.53082

**Subjects**

Primary: 47L10: Algebras of operators on Banach spaces and other topological linear spaces

Secondary: 46H10: Ideals and subalgebras 46J05: General theory of commutative topological algebras

**Keywords**

algebra of Banach space operators maximal commutative subalgebra multiplications on Banach spaces

#### Citation

Żelazko, Wiesław. All maximal commutative subalgebras occur in $L(X)$ uncountably many times. Funct. Approx. Comment. Math. 53 (2015), no. 2, 189--192. doi:10.7169/facm/2015.53.2.2. https://projecteuclid.org/euclid.facm/1450389051