Spectral Properties of n-perinormal operators

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...

Spectral Properties of Operators

It is well known that the identity is an operator with the following property: if the operator, initially defined on an n-dimensional Banach space V , can be extended to any Banach space with norm 1, then V is isometric to (n) ∞ . We show that the set of all such operators consists precisely of those with spectrum lying in the unit circle. This result answers a question raised in [5] for comple...

Spectral Properties of Hypoelliptic Operators

We study hypoelliptic operators with polynomially bounded coefficients that are of the form K = ∑m i=1 X i Xi + X0 + f , where the Xj denote first order differential operators, f is a function with at most polynomial growth, and X i denotes the formal adjoint of Xi in L. For any ε > 0 we show that an inequality of the form ‖u‖δ,δ ≤ C(‖u‖0,ε + ‖(K + iy)u‖0,0) holds for suitable δ and C which are...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Spectral Properties of Limit-periodic Schrödinger Operators

We investigate the spectral properties of Schrödinger operators in `2(Z) with limit-periodic potentials. The perspective we take was recently proposed by Avila and is based on regarding such potentials as generated by continuous sampling along the orbits of a minimal translation of a Cantor group. This point of view allows one to separate the base dynamics and the sampling function. We show tha...