Some notes on orthogonally additive polynomials
نویسندگان
چکیده
We provide two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into convex bornological space using separately polynomial identities Kusraeva involving the root mean power and geometric mean. Furthermore, it is shown that on whenever positive cone. These results improve recent by G. Buskes author.
منابع مشابه
Orthogonally Additive Polynomials on C*-algebras
Let A be a C*-algebra which has no quotient isomorphic to M2(C). We show that for every orthogonally additive scalar nhomogeneous polynomials P on A such that P is Strong* continuous on the closed unit ball of A, there exists φ in A∗ satisfying that P (x) = φ(x), for each element x in A. The vector valued analogue follows as a corollary.
متن کاملOrthogonally Additive Polynomials on Spaces of Continuous Functions
We show that, for every orthogonally additive homogeneous polynomial P on a space of continuous functions C(K) with values in a Banach space Y , there exists a linear operator S : C(K) −→ Y such that P (f) = S(f). This is the C(K) version of a related result of Sundaresam for polynomials on Lp spaces.
متن کاملLecture Notes on Polynomials
Looking at the examples in (2.1), we see that the degree of the first polynomial is 2, the second one has degree 16, etc. A number of operations can be performed with polynomials. Given a polynomial p(z) and a complex number c, the polynomial c p(z) is obtained by multiplying each coefficient in p(z) by c. Given two polynomials p(z) and q(z), their sum is defined by adding the coefficients of c...
متن کاملOn Counting Polynomials of Some Nanostructures
The Omega polynomial(x) was recently proposed by Diudea, based on the length of strips in given graph G. The Sadhana polynomial has been defined to evaluate the Sadhana index of a molecular graph. The PI polynomial is another molecular descriptor. In this paper we compute these three polynomials for some infinite classes of nanostructures.
متن کاملSome notes on distributions
Formally, distributions are usually defined as continuous linear functions on a certain topological vector space of “test functions”. However, it is not surprising that useful mathematical objects such as distributions also have a natural, concrete description. We shall start from this viewpoint, and later explain the abstraction to topological vector spaces, and explain why the latter is impor...
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: Quaestiones Mathematicae
سال: 2021
ISSN: ['1727-933X', '1607-3606']
DOI: https://doi.org/10.2989/16073606.2021.1953631