Literature for this section is for instance Sugiura [3, Ch. 1]. Let G be a group. Representations of G can be defined on any vector space (possibly infinite dimensional) over any field, but we will only consider representations on finite dimensional complex vector spaces. Let V be a finite dimensional complex vector space. Let GL(V ) be the set of all invertible linear transformations of V . Th...

Let G be a group. Representations of G can be defined on any vector space (possibly infinite dimensional) over any field, but we will only consider representations on finite dimensional complex vector spaces. Let V be a finite dimensional complex vector space. Let GL(V ) be the set of all invertible linear transformations of V . This is a group under composition. If V has dimension n and if we ...

A weak group element is introduced in a proper *-ring. Several equivalent conditions of elements are investigated. We prove that an pseudo core invertible if it both partial isometry and invertible. Reverse order law additive property the inverse presented. Finally, under certain assumption on a, a◯Wa∗=a∗a◯W presented by using normality part its group-EP decomposition.

We give a calculation of Picard groups Pic2 of K(2)-local invertible spectra and Pic(L2) of E(2)-local invertible spectra, both at the prime 3. The main contribution of this paper is to calculation the subgroup κ2 of invertible spectra X with (E2)∗X ∼= (E2)∗S as continuous modules over the Morava stabilizer group G2.

We endow the group of invertible Fourier integral operators on an open manifold with the structure of an ILH Lie group. This is done by establishing such structures for the groups of invertible pseudodiierential operators and contact transformations on an open manifold of bounded geometry, and gluing those together via a local section.

We endow the group of invertible Fourier integral operators on an open manifold with the structure of an ILH Lie group. This is done by establishing such structures for the groups of invertible pseudodifferential operators and contact transformations on an open manifold of bounded geometry, and gluing those together via a local section.