Pusz–Woronowicz’s functional calculus revisited
نویسندگان
چکیده
This note is a complement to Pusz–Woronowicz’s works on functional calculus for two positive forms from the viewpoint of operator theory. Based an elementary, self-contained and purely Hilbert space explanation their calculus, we show that any connection type operations (including perspectives) are captured by calculus.
منابع مشابه
The Do-Calculus Revisited
The do-calculus was developed in 1995 to facilitate the identification of causal effects in non-parametric models. The completeness proofs of [Huang and Valtorta, 2006] and [Shpitser and Pearl, 2006] and the graphical criteria of [Tian and Shpitser, 2010] have laid this identification problem to rest. Recent explorations unveil the usefulness of the do-calculus in three additional areas: mediat...
متن کاملEvent Calculus Planning Revisited
In 1969 Cordell Green presented his seminal description of planning as theorem proving with the situation calculus. The most pleasing feature of Green's account was the negligible gap between high-level logical specification and practical implementation. This paper attempts to reinstate the ideal of planning via theorem proving in a modern guise. In particular, I will show that if we adopt the ...
متن کاملStochastic Pi-calculus Revisited
We develop a version of stochastic Pi-calculus endowed with a structural operational semantics expressed in terms of measure theory. The paper relies on two observations: (i) the structural congruence organizes a measurable space of processes and (ii) a well behaved SOS associates to each process, in a specified rate environment, a behaviour defined by a set of measures over the measurable spac...
متن کاملWeakest Precondition Calculus, Revisited using Why3
This report has two objectives. First, we present an original method of proof of soundness of a weakest precondition calculus, based on the notion of blocking semantics. The method mimics, at the level of logic specifications, the classical proof of type soundness. Moreover, the proof is performed formally using the Why3 environment for deductive verification, and we illustrate, along the devel...
متن کاملThe Principles of Ambient Calculus Revisited
The paper presents a foundational analysis of the class of ambient calculi focussing on the spatial structures of the processes they can describe. We propose sound correct set-theoretical models for different types of ambient calculi (involving recursion, denumerable parallel composition, etc) by using special types of coalgebras labelled flat systems of equations of set theory. These models he...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Scientiarum Mathematicarum
سال: 2021
ISSN: ['0324-5462', '2064-8316', '0001-6969']
DOI: https://doi.org/10.14232/actasm-021-263-6