## Banach algebra

An algebra in which the vector space is a Banach space.

Last updated: 1997-02-25

## Banach inverse mapping theorem

In a Banach space the inverse to a continuous linear mapping is continuous.

Last updated: 1998-06-25

## Banach space

A complete normed vector space. Metric is induced by the norm: d(x,y) = ||x-y||. Completeness means that every Cauchy sequence converges to an element of the space. All finite-dimensional real and complex normed vector spaces are complete and thus are Banach spaces.

Using absolute value for the norm, the real numbers are a Banach space whereas the rationals are not. This is because there are sequences of rationals that converges to irrationals.

Several theorems hold only in Banach spaces, e.g. the Banach inverse mapping theorem. All finite-dimensional real and complex vector spaces are Banach spaces. Hilbert spaces, spaces of integrable functions, and spaces of absolutely convergent series are examples of infinite-dimensional Banach spaces. Applications include wavelets, signal processing, and radar.

[Robert E. Megginson, "An Introduction to Banach Space Theory", Graduate Texts in Mathematics, 183, Springer Verlag, September 1998].

Last updated: 2000-03-10

It is possible to cut a solid ball into finitely many pieces (actually about half a dozen), and then put the pieces together again to get two solid balls, each the same size as the original.

This paradox is a consequence of the Axiom of Choice.

Last updated: 1995-03-29

## banana label

<jargon>

The labels used on the sides of macrotape reels, so called because they were shaped roughly like blunt-ended bananas. This term, like macrotapes themselves, is obsolete.

[Jargon File]

Last updated: 2007-10-17

banana problem

## banana problem

From the story of the little girl who said "I know how to spell "banana", but I don't know when to stop". Not knowing where or when to bring a production to a close (compare fencepost error). One may say "there is a banana problem" of an algorithm with poorly defined or incorrect termination conditions, or in discussing the evolution of a design that may be succumbing to featuritis (see also creeping elegance, creeping featuritis).

HAKMEM item 176 describes a banana problem in a Dissociated Press implementation. Also, see one-banana problem for a superficially similar but unrelated usage.

Last updated: 2010-03-20

## bandwidth

The difference between the highest and lowest frequencies of a transmission channel (the width of its allocated band of frequencies).

The term is often used erroneously to mean data rate or capacity - the amount of data that is, or can be, sent through a given communications circuit per second.

[How is data capacity related to bandwidth?]

[Jargon File]

Last updated: 2001-04-24

## bang

A spoken name for the exclamation mark character ("!" ASCII 33) when used as a piece of technical syntax (e.g. in a bang path) rather than to mark a command or exclamation.

[Jargon File]

Last updated: 1995-01-31

## bang on

(Or "pound on"). To stress-test a piece of hardware or software: "I banged on the new version of the simulator all day yesterday and it didn't crash once. I guess it is ready for release."

[Jargon File]

## bang path

1. An old-style UUCP electronic-mail address naming a sequence of hosts through which a message must pass to get from some assumed-reachable location to the addressee (a "source route"). So called because each hop is signified by a bang sign (exclamation mark). Thus, for example, the path

``` ...!bigsite!foovax!barbox!me

```
directs people to route their mail to computer bigsite (presumably a well-known location accessible to everybody) and from there through the computer foovax to the account of user me on barbox.

Before autorouting mailers became commonplace, people often published compound bang addresses using the convention (see glob) to give paths from *several* big computers, in the hope that one's correspondent might be able to get mail to one of them reliably. e.g.

``` ...!{seismo, ut-sally, ihnp4}!rice!beta!gamma!me

```
Bang paths of 8 to 10 hops were not uncommon in 1981. Late-night dial-up UUCP links would cause week-long transmission times. Bang paths were often selected by both transmission time and reliability, as messages would often get lost.

2. A shebang.

Last updated: 1998-05-06

## banner

1. The title page added to printouts by most print spoolers. Typically includes user or account ID information in very large character-graphics capitals. Also called a "burst page", because it indicates where to burst (tear apart) fanfold paper to separate one user's printout from the next.

2. A similar printout generated (typically on multiple pages of fan-fold paper) from user-specified text, e.g. by a program such as Unix's "banner".

3. splash screen.

[Jargon File]

Last updated: 1994-11-28

## Banyan

<company>

A personal computer networking company, best known for its "Vines" products for local area networks.