To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

From Wikipedia, the free encyclopedia

In mathematics, and specifically in functional analysis, the Lp sum of a family of Banach spaces is a way of turning a subset of the product set of the members of the family into a Banach space in its own right. The construction is motivated by the classical Lp spaces.[1]

Definition

Let be a family of Banach spaces, where may have arbitrarily large cardinality. Set

the product vector space.

The index set becomes a measure space when endowed with its counting measure (which we shall denote by ), and each element induces a function

Thus, we may define a function

and we then set
together with the norm

The result is a normed Banach space, and this is precisely the Lp sum of

Properties

  • Whenever infinitely many of the contain a nonzero element, the topology induced by the above norm is strictly in between product and box topology.
  • Whenever infinitely many of the contain a nonzero element, the Lp sum is neither a product nor a coproduct.

References

  1. ^ Helemskii, A. Ya. (2006). Lectures and Exercises on Functional Analysis. Translations of Mathematical Monographs. American Mathematical Society. ISBN 0-8218-4098-3.
This page was last edited on 7 March 2023, at 18:51
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.