pre-Hilbert space

pre-Hilbert space

[prē′hil·bərt ‚spās]
(mathematics)
inner-product space
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
Mentioned in ?
References in periodicals archive ?
([2], Proposition 1.14.) If a normed real vector space (X, ||*||) is CAT([kappa]), for some [kappa] [member of] R, then it is a pre-Hilbert space.
But according to Theorem 2.1 E is a CAT(K), for some [kappa] [member of] R, if and only if (E, ||*||) is a pre-Hilbert space. In other words, our definition gives a new class of CAT(0) metric spaces provided (E, ||*||) is not a pre-Hilbert vector space.
Generalized CAT(0) spaces

Encyclopedia browser ?
Full browser ?