Talk:Operator algebra

It would be nice to have at least one example of an Operator Algebra. Most of the other pages on mathematical objects list a few examples. CarlFeynman (talk) 23:06, 4 May 2011 (UTC)[reply]

This page says "Operator algebras are in general non-commutative rings" Whereas, the page about rings say rings have to have the property that their operators are commutative. What gives? —Preceding unsigned comment added by 76.23.104.212 (talk) 20:44, 13 May 2011 (UTC)[reply]

In general, a ring's product is not necessarily commutative. Some authors, the ones who will only be talking about commutative rings, include commutativity in the definition for convenience. It's just a matter of convention. The phrase "non-commutative ring" refers to a ring whose product is not assumed to be commutative. However, I think the Wikipedia page on rings should not include commutativity since the "standard" definition does not. 70.30.23.131 (talk) 16:53, 5 June 2014 (UTC)[reply]

Extremely bad introduction

The first two paragraphs of the article are as follows

"In functional analysis, an operator algebra is an algebra of continuous linear operators on a topological vector space with the multiplication given by the composition of mappings.

"The results are phrased in algebraic terms, while the techniques are highly analytic. Although it is usually classified as a branch of functional analysis, it has direct applications to representation theory, differential geometry, quantum statistical mechanics, quantum information, and quantum field theory."

This writing is inappropriate for several reasons.

1. When the first sentence describes only a mathematical concept ("an operator algebra"), nobody knows what Wikipedia is talking about when it then begins the next paragraph with "The results". The results of what??? The article has not stated what it is talking about.

Most Wikipedia readers will not understand this unless they are mathematicians. Most Wikipedia readers have no idea what the word "results" refers to here.

2. The second sentence in the second quoted paragraph is just as bad, if not worse:

"Although it is usually classified as a branch of functional analysis, it has direct applications to ..."

Almost nobody reading Wikipedia will have the slightest idea what the word "it" means each time it is used in this sentence.

(Helpful hint: When using a pronoun, make sure it has an antecedent.)2600:1700:E1C0:F340:DD66:DEDF:A0A1:935D (talk) 20:39, 24 October 2018 (UTC)[reply]

Is it better now? – Tea2min (talk) 08:20, 25 October 2018 (UTC)[reply]