Polar decompositions of quaternion matrices in indefinite inner product spaces

Polar decompositions of quaternion matrices with respect to a given indefinite inner product are studied. Necessary and sufficient conditions for the existence of an $H$-polar decomposition are found. In the process, an equivalent to Witt's theorem on extending $H$-isometries to $H$-unitary matrices is given for quaternion matrices.

Norms on Quotient Spaces of The 2-Inner Product Space

This paper discussed about construction of some quotients spaces of the 2-inner product spaces. On those quotient spaces, we defined an inner product with respect to a linear independent set. These inner products was derived from the -inner product. We then defined a norm which induced by the inner product in these quotient spaces.

On Lipschitz continuity with respect to the Poincaré metric of linear contractions between Möbius gyrovector spaces

For every linear operator between inner product spaces whose operator norm is less than or equal to one, we show that the restriction to the Möbius gyrovector space is Lipschitz continuous with respect to the Poincaré metric. Moreover, the Lipschitz constant is precisely the operator norm.

Some Bessel type additive inequalities in inner product spaces

"In this paper we obtain some additive inequalities related to the cele- brated Bessel's inequality in inner product spaces. They complement the results obtained by Boas-Bellman, Bombieri, Selberg and Heilbronn, which have been applied for almost orthogonal series and in Number Theory."