Measurable Subspaces and Subalgebras1

Some Results concerning Frames Associated with Measurable Spaces

In this note some necessary or/and sufficient conditions for the perturbation of a (Ω, μ)-frame are given. We also discussed (Ω, μ)-frames of subspaces.

ε-weakly Chebyshev subspaces and quotient spaces

On an Inequality of A. Grothendieck

In 1955, A. Grothendieck proved a basic inequality which shows that any bounded linear operator between L(μ)-spaces maps (Lebesgue-) dominated sequences to dominated sequences. An elementary proof of this inequality is obtained via a new decomposition principle for the lattice of measurable functions. An exposition is also given of the M. Lévy extension theorem for operators defined on subspace...

USING FRAMES OF SUBSPACES IN GALERKIN AND RICHARDSON METHODS FOR SOLVING OPERATOR EQUATIONS

‎In this paper‎, ‎two iterative methods are constructed to solve the operator equation $ Lu=f $ where $L:Hrightarrow H $ is a bounded‎, ‎invertible and self-adjoint linear operator on a separable Hilbert space $ H $‎. ‎ By using the concept of frames of subspaces‎, ‎which is a generalization of frame theory‎, ‎we design some  algorithms based on Galerkin and Richardson methods‎, ‎and then we in...

Maximal prehomogeneous subspaces on classical groups

Suppose $G$ is a split connected‎ ‎reductive orthogonal or symplectic group over an infinite field‎ ‎$F,$ $P=MN$ is a maximal parabolic subgroup of $G,$ $frak{n}$ is‎ ‎the Lie algebra of the unipotent radical $N.$ Under the adjoint‎ ‎action of its stabilizer in $M,$ every maximal prehomogeneous‎ ‎subspaces of $frak{n}$ is determined‎.