162 research outputs found
An operator extension of the parallelogram law and related norm inequalities
We establish a general operator parallelogram law concerning a
characterization of inner product spaces, get an operator extension of Bohr's
inequality and present several norm inequalities. More precisely, let
be a -algebra, be a locally compact Hausdorff space
equipped with a Radon measure and let be a continuous
field of operators in such that the function is
norm continuous on and the function is integrable. If
is a measurable function such that
for all , then we show that
\begin{align*} \int_T\int_T&\left|\alpha(t,s) A_t-\alpha(s,t)
A_s\right|^2d\mu(t)d\mu(s)+\int_T\int_T\left|\alpha(t,s) B_t-\alpha(s,t)
B_s\right|^2d\mu(t)d\mu(s) \nonumber &= 2\int_T\int_T\left|\alpha(t,s)
A_t-\alpha(s,t) B_s\right|^2d\mu(t)d\mu(s) -
2\left|\int_T(A_t-B_t)d\mu(t)\right|^2\,. \end{align*}Comment: 9 pages; To appear in Math. Inequal. Appl. (MIA
Hyers-Ulam-Rassias Stability of Generalized Derivations
The generalized Hyers--Ulam--Rassias stability of generalized derivations on
unital Banach algebras into Banach bimodules is established.Comment: 9 pages, minor changes, to appear in Internat. J. Math. Math. Sc
Matrix Hermite-Hadamard type inequalities
We present several matrix and operator inequalities of Hermite-Hadamard type.
We first establish a majorization version for monotone convex functions on
matrices. We then utilize the Mond-Pecaric method to get an operator version
for convex functions. We also present some applications. Finally we obtain an
Hermite-Hadamard inequality for operator convex functions, positive linear maps
and operators acting on Hilbert spaces.Comment: 13 pages, revised versio
On (Co)Homology of Triangular Banach Algebras
Suppose that A and B are unital Banach algebras with units 1_A and 1_B,
respectively, M is a unital Banach A-B-bimodule, T=Tri(A,M,B) is the triangular
Banach algebra, X is a unital T-bimodule, X_{AA}=1_AX1_A, X_{BB}=1_BX1_B,
X_{AB}=1_AX1_B and X_{BA}=1_BX1_A. Applying two nice long exact sequences
related to A, B, T, X, X_{AA}, X_{BB}, X_{AB} and X_{BA} we establish some
results on (co)homology of triangular Banach algebras.Comment: 10 page
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