Generalized derivations and general relativity

Generalized Riemann Spaces and General Relativity.

spectrum of K, and fixed t > 0. As a consequence, u(-, t) lies in the range of (K tI), and by Theorem 3 of Paper I, after a replacement on a set of measure zero, u(-, t) lies in C"T(D). If Eg(x) is the smooth representative of its equivalence class in L2' r(D), for any Borel set A in El lying in the interval XI < a, by Theorem 3 of Paper I, IE(A)g(x)I = I(K, I)-j(K R I)jE(A)g(x)I < C(oaI + I I)...

Generalized Derivations on Modules

Generalized observers and velocity measurements in General Relativity

To resolve some unphysical interpretations related to velocity measurements by static observers, we discuss the use of generalized observer sets, give a prescription for defining the speed of test particles relative to these observers, and show that, for any locally inertial frame, the speed of a freely falling material particle is always less than the speed of light at the Schwarzschild black ...

Generalized Derivations on Modules *

Let A be a Banach algebra and M be a Banach left A-module. A linear map δ : M → M is called a generalized derivation if there exists a derivation d : A → A such that δ(ax) = aδ(x) + d(a)x (a ∈ A,x ∈ M). In this paper, we associate a triangular Banach algebra T to Banach A-module M and investigate the relation between generalized derivations on M and derivations on T . In particular, we prove th...

Nearly Generalized Jordan Derivations

Let A be an algebra and let X be an A-bimodule. A C−linear mapping d : A → X is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) δ : A → X such that d(a) = ad(a) + δ(a)a for all a ∈ A. The main purpose of this paper to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.