On $n$-norms and bounded $n$-linear functionals in a hilbert space

Fungsional Linear-2 Dalam Ruang Norm-2

“…Later, many researchers studied some properties and aspects in 2-normed spaces or nnormed spaces. For instance we can see at [1,2,7,8,9,10,11,12,13,14,15,18,19]. In this paper we will observe about bounded 2-linear functional in 2-normed spaces.…”

“…Kemudian Misiak di tahun 1989 memperkenalkan ruang hasil kali dalam-n ( ≥ 2) [16]. Setelah itu, banyak peneliti yang mengkaji sifat-sifat ataupun aspek-aspek dalam ruang norm-2 maupun ruang norm-n. Hal ini dapat dilihat pada beberapa penelitian dalam [1,2,7,8,9,10,11,12,13,14,15,18,19]. Dalam penelitian ini aspek yang akan ditinjau adalah fungsional linear-2 terbatas pada ruang norm-2.…”

Riesz representation theorem on generalized n-inner product spaces

“…, − being multilinear induces multilinear property of the functional f (a 1 ,...,an) . The converse of this result, exposed by [3] as Riesz type representation theorem, is an interesting problem to be addressed. Unfortunately the expectation that any bounded n-linear functional on a real separable Hilbert space can be represented by n unique vectors is not true as shown in the following example.…”

“…Gozali etal. [3] exposed a question whether Riesz type representation theorem holds on standard generalized n-inner product spaces; that is whether any bounded n-linear functional on a separable Hilbert space can be represented by n unique vectors. We show that the question has negative answer and prove an enhancement of Riesz representation theorem on standard generalized n-inner product spaces.…”

ON STRONG AND WEAK CONVERGENCE IN $n-$HILBERT SPACES

“…The corresponding theory of n-inner product spaces was then established by Misiak ([10]). Since then, various aspects of the theory have been studied, for instance the study of Mazur-Ulam theorem and Aleksandrov problem in n-normed spaces are done in [1,2], the study of operators in n-Banach space is done in [5,11], and many others.…”