On operators which are adjoint to each other

Monads for which Structures are Adjoint to Units

We present here the equational two-dimensional categorical algebra which describes the process of freely completing a category under some class of limits or colimits. It is crystallized out of the authors 1967 dissertation [6] (revised form [7]). I presented a purely equational aspect of that already in 1973 [9], [10] , and the present note is in some sense identical to that, but with some furt...

We are very much like each other

A Framework in which Robots and Humans Help Each Other

Within the context of human/multi-robot teams, the “help me help you” paradigm offers different opportunities. A team of robots can help a human operator accomplish a goal, and a human operator can help a team of robots accomplish the same, or a different, goal. Two scenarios are examined here. First, a team of robots helps a human operator search a remote facility by recognizing objects of int...

Adjoint and self - adjoint differential operators on graphs ∗

A differential operator on a directed graph with weighted edges is characterized as a system of ordinary differential operators. A class of local operators is introduced to clarify which operators should be considered as defined on the graph. When the edge lengths have a positive lower bound, all local self-adjoint extensions of the minimal symmetric operator may be classified by boundary condi...

Multiplicative Maps on Ideals of Operators Which Are Local Automorphisms

We present the following reflexivity-like result concerning the automorphism group of the C∗-algebra B(H), H being a separable Hilbert space. Let φ : B(H) → B(H) be a multiplicative map (no linearity or continuity is assumed) which can be approximated at every point by automorphisms of B(H) (these automorphisms may, of course, depend on the point) in the operator norm. Then φ is an automorphism...