Another characterization of Hilbert spaces

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

On the Decomposition of Hilbert Spaces

Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition fo...

Multipliers of generalized frames in Hilbert spaces

Characterization of splitting for Fréchet-Hilbert spaces via interpolation

Based on the methods from interpolation theory we give a characterization of pairs (E,F ) of Fréchet-Hilbert spaces so that for each Fréchet-Hilbert space G each short exact sequence 0 −→ F −→ G −→ E −→ 0 splits. This characterization essentially depends on a key condition (S) of an interpolation nature. An equivalent description of (S) in terms of appropriate families of interpolation function...

Hilbert spaces

• Pre-Hilbert spaces: definition • Cauchy-Schwarz-Bunyakowski inequality • Example: spaces ` • Triangle inequality, associated metric, continuity issues • Hilbert spaces, completions, infinite sums • Minimum principle • Orthogonal projections to closed subspaces • Orthogonal complements W⊥ • Riesz-Fischer theorem on linear functionals • Orthonormal sets, separability • Parseval equality, Bessel...