Vol. 2 No. 3 (2009)

We consider a linear bounded operator in infnite dimensional separable Hilbert space satisfying some conditions. We prove formulas that can be used to calculate the index of this operator.

n this paper we show that h-prime and h-semiprime ideals in a Nobusawa $\Gamma$-semiring are preserved by the functions $^{*'}(~)$, $^{+'}(~)$, $^{*}(~)$, $^{+}(~)$, $\Gamma (~)$ and S( ). This preservation property is then used to characterize h-prime and h-semiprime ideals in matrix semiring $\left(\begin{array}{ll} R & \Gamma \\ S & L \end{array} \right)$. Moreover, characterization theorems of h-regular and H-Noetherian $\Gamma-$semirings have been obtained.

By using reverse H\"{o}lder's inequalities we obtain reverse weighted $L_p$ norm inequalities for various iterated convolutions.