Sadayuki Yamamuro

A note on d -ideals in some near-algebras

Let E be a real Banach space. The set of all continuous linear mappings of E into E is a Banach algebra under the usual algebraic operations and the operator bound as norm. We denote this Banach algebra by ℒ, if E is a separate Hilbert space .

A Note on Semigroups of Mappings on Banach Spaces

In a series of papers K. D. Magill, Jr. (see [1] and its references) has proved that, in various semigroups of mappings on topological spaces, every automorphism is inner , where an automorphism φ of a semigroup A is a bijection of A such that for all ƒ and g in A , and it is said to be inner if there exists a bijection h ∈ A such that h −1 (the inverse of h ) belongs to A and for every ƒ ∈ A .

Notes on the inverse mapping theorem in locally convex spaces

Several problems arising from a functional analytic study on Omoris inverse mapping theorem are considered arriving at an inverse mapping theorem in locally convex spaces.

A note on Omori-Lie groups

The theory of differentiation in locally convex spaces constructed by the author in Memoirs Amer. Math. Soc. 17 (1979) is used to give a new form of the definition of Omori-Lie groups.

A note on the omega lemma

A class of locally convex spaces, a B -subfamily of finite order, is defined and the omega lemma for spaces belonging to this family is proved.

On Homomorphisms of an Orthogonally Decomposable Hilbert Space II

A hyperfinite von Neumann algebra satisfies the condition that every o.d. homomorphism is a normal operator if and only if it is a factor of type I n .

On the surjectivity of linear maps on locally convex spaces

The aim of this note is to investigate the structure of general surjectivity problem for a continuous linear map between locally convex spaces. We shall do so by using the method introduced in Yamamuro (1980). Its basic notion is that of calibrations which has been introduced in Yamamuro (1975), studied in detail in Yamamuro (1979) and appliced to several problems in Yamamuro (1978) and Yamamuro (1979a).

On the semigroup of Hadamard differentiable mappings

The main purpose of this paper is to prove that every automorphism of the semigroup of all Hadamard-differentiable mappings of a separable real Banach space into itself is inner. This generalizes the results of [7] which is a generalization of a result proved by Magill, Jr. [5].

A Note on Finite-Dimensional Differentiable Mappings

Let E be a real infinite-dimensional Banach space. Let ℒ be the Banach algebra of all continuous linear mappings of E into itself with topology defined by the norm:

Notes on differential calculus in topological linear spaces, III

Throughout this note, let E, F and G be locally convex Hausdorff spaces over the real number field R . We denote real numbers by Greek letters. The sets of all continuous semi-norms on E and F will be denoted by P ( E ) and P ( F ) respectively, and A will always stand for an open subset of E .