We consider, using various tensor norms, the completed tensor product of two unital lmc algebras one of which is commutative. Our main result shows that when the tensor product of two Q-algebras is an lmc algebra, then it is a Q-algebra if and only if pointwise invertibility implies invertibility (as in the Gelfand theory). This is always the case for Fréchet algebras.
We study the subset in a unital C*-algebra composed of elements a such that is invertible, where denotes the Moore-Penrose inverse of a. A distinguished subset of this set is also investigated. Furthermore we study sequences of elements belonging to the aforementioned subsets.
We study discontinuous invertibility preserving linear mappings from a Banach algebra into the algebra of n × n matrices and give an explicit representation of such a mapping when n = 2.
Let L¹(G)** be the second dual of the group algebra L¹(G) of a locally compact group G. We study the question of involutions on L¹(G)**. A new class of subamenable groups is introduced which is universal for all groups. There is no involution on L¹(G)** for a subamenable group G.
Suppose that a real nonatomic function space on is equipped with two rearrangement-invariant norms and . We study the question whether or not the fact that is isometric to implies that for all in . We show that in strictly monotone Orlicz and Lorentz spaces this is equivalent to asking whether or not the norms are defined by equal Orlicz functions, respĿorentz weights. We show that the above implication holds true in most rearrangement-invariant spaces, but we also identify a class...
Isometric Sobolev spaces on finite graphs are characterized. The characterization implies that the following analogue of the Banach-Stone theorem is valid: if two Sobolev spaces on 3-connected graphs, with the exponent which is not an even integer, are isometric, then the corresponding graphs are isomorphic. As a corollary it is shown that for each finite group and each p which is not an even integer, there exists n ∈ ℕ and a subspace whose group of isometries is the direct product × ℤ₂.
We investigate isometric composition operators on the weighted Dirichlet space with standard weights , . The main technique used comes from Martín and Vukotić who completely characterized the isometric composition operators on the classical Dirichlet space . We solve some of these but not in general. We also investigate the situation when is equipped with another equivalent norm.
In this article, we formalize isometric differentiable functions on real normed space [17], and their properties.