Sentence examples similar to index of operators from inspiring English sources

Let E be a Banach space and let K ⊂ E be a closed convex cone in E. Let L : K → K be a completely continuous operator and let i(L, K r, K) denote the fixed point index of operator L. (i) If μLu ≠ u for any u ∈ ∂K r and 0 < μ ≤ 1, then.

There are no numbers, arithmetic is to be construed as a calculus in which one manipulates exponents or indices of operators.

Trace formulas are used for evaluation of first eigenvalues, they have application to inverse problems, index theory of operators and so forth.

The index formula of scattering operators of the previous paper of the author (T. Matsui, The index of scattering operators of Dirac equations, Commun. Math. Phys.110 (1987) 553 571) is shown to hold for a wider class of potentials which contains both gauge potentials with compactly supported energy and instantontype potentials.

We compute the equivariant cohomology Connes Karoubi character of the index of elliptic operators along the leaves of the foliation of a flat bundle.

We characterize those operators the domain and range of which can be renormed so that the operator has property in terms of the Szlenk index of the operator and its adjoint.

We introduce and study the Bourgain index of an operator between two Banach spaces.

We characterize the ordinals which occur as the index of an operator and establish exactly when the defined classes are closed.

A formula for the index of the operator, i.e., the difference between the dimensions of the kernel and cokernel is obtained.

The analysis proceeds by imbedding Tϑx in a type II∞ factor and computing the real-valued index of the operator à la Connes.

We give a complete description of renorming results for these properties in terms of the Szlenk index of the operator, as well as a complete description of the duality between these two properties.