commutator

Let A, B, X, and Y be bounded linear operators on a complex Hilbert space. It is shown that where w (·) and‖·‖ are the numerical radius and the usual operator norm, respectively. This inequality includes and improves upon earlier numerical radius inequalities proved in this context. Applications of this inequality are given to obtain new numerical radius inequalities for commutators of self-adjoint and positive operators.

It is well known that the induction coil was invented in the mid-1830s, but its most significant im-provements were made between the late 1830s and 1851. During these years a lot of research was aimed at improving the functionality and effectiveness of the device. In Italy one of the very first attempts at improvement was made first by an instrument maker from Milan, Carlo Dell’Acqua, and secondly, by a priest from Verona, Vincenzo Vignola. In 1851, Vignola was awarded the gold medal from the Academy of Agriculture, Arts and Commerce of Verona for having introduced im-portant and useful changes to the Callan electromotor. This event opened up the discovery of a number of very interesting, unpublished hand-written documents, as well as the discovery of the device itself, provided with an almost unique self-acting commutator-interrupter system. Today this apparatus is preserved at the Physics Museum “Antonio Maria Traversi ” in Venice.

ABSTRACT The FFT is an important core to which we couple an M-path partitioned filter and commutator to build high performance spectrum analyzers and channelized transmitters and receivers. With slight modifications of the system the channelizer and spectrum analyzer can perform secondary processing tasks such as arbitrary sample rate changes. Output sample rates can be adjusted to be a multiple of channel spacing or a multiple of the channel symbol rate. With minor additional processing the channelizer can also coherently combine signals from adjacent frequency bands to synthesize arbitrary bandwidth super channels from standard prototype channels.