Bs space

Bs space

In the mathematical field of functional analysis, the space bs consists of all infinite sequences ("x""i") of real or complex numbers such that

:sup_nleft|sum_{i=1}^n x_i ight|

is finite. The set of such sequences forms a normed space with the vector space operations defined componentwise, and the norm given by

:left|x ight|_{bs} = sup_nleft|sum_{i=1}^n x_i ight|.

Furthermore, with respect to metric induced by this norm, "bs" is complete: it is a Banach space.

The space of all sequences ("x""i") such that the series

:sum_{i=1}^infty x_i

is convergent (possibly conditionally) is denoted by "cs". This is a closed vector subspace of "bs", and so is also a Banach space with the same norm.

The space "bs" is isometrically isomorphic to ℓ via the mapping

:T(x_1,x_2,dots) = (x_1,x_1+x_2,x_1+x_2+x_3,dots).

Furthermore, "c" is the image of "cs" under "T".

References

*.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

  • Space tourism — is the recent phenomenon of tourists paying for flights into space pioneered by Russia.As of 2008, orbital space tourism opportunities are limited and expensive, with only the Russian Space Agency providing transport. The price for a flight… …   Wikipedia

  • Space debris — populations seen from outside geosynchronous orbit (GEO). Note the two primary debris fields, the ring of objects in GEO, and the cloud of objects in low earth orbit (LEO) …   Wikipedia

  • Space music — Space music, also spelled spacemusic, is an umbrella term used to describe music that evokes a feeling of contemplative spaciousness. In fact, almost any music with a slow pace and space creating sound images could be called spacemusic. Stephen… …   Wikipedia

  • Space-Marine — (Warhammer 40,000) Dans l univers de fiction Warhammer 40,000 créé par Games Workshop, les Space Marines (ou Adeptus Astartes) sont des soldats d élite humains, modifiés et équipés des derniers raffinements technologiques, et qui combattent au… …   Wikipédia en Français

  • Space-Marines — Space Marine (Warhammer 40,000) Dans l univers de fiction Warhammer 40,000 créé par Games Workshop, les Space Marines (ou Adeptus Astartes) sont des soldats d élite humains, modifiés et équipés des derniers raffinements technologiques, et qui… …   Wikipédia en Français

  • Space Marine (Warhammer 40000) — Space Marine (Warhammer 40,000) Dans l univers de fiction Warhammer 40,000 créé par Games Workshop, les Space Marines (ou Adeptus Astartes) sont des soldats d élite humains, modifiés et équipés des derniers raffinements technologiques, et qui… …   Wikipédia en Français

  • Space Marines — Space Marine (Warhammer 40,000) Dans l univers de fiction Warhammer 40,000 créé par Games Workshop, les Space Marines (ou Adeptus Astartes) sont des soldats d élite humains, modifiés et équipés des derniers raffinements technologiques, et qui… …   Wikipédia en Français

  • Space marine (warhammer 40,000) — Dans l univers de fiction Warhammer 40,000 créé par Games Workshop, les Space Marines (ou Adeptus Astartes) sont des soldats d élite humains, modifiés et équipés des derniers raffinements technologiques, et qui combattent au péril de leurs vies… …   Wikipédia en Français

  • Space exploration — is the use of astronomy and space technology to explore outer space. [cite web | url = http://adc.gsfc.nasa.gov/adc/education/space ex/exploration.html | title = How Space is Explored | publisher = NASA] Physical exploration of space is conducted …   Wikipedia

  • Space science — is an all encompassing term that describes all of the various science fields that are concerned with the study of the Universe, generally also meaning excluding the Earth and outside of the Earth s atmosphere . Originally, all of these fields… …   Wikipedia

  • Space-Shuttle — Die Atlantis startet zur Mission STS 115 Orbiter Länge 37,24 m Spannweite 23,79 m Startgewicht (maximal) 109.000 kg …   Deutsch Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”