Janko Marovt

Bio: Janko Marovt is an academic researcher from University of Maribor. The author has contributed to research in topics: Bounded function & Hilbert space. The author has an hindex of 7, co-authored 34 publications receiving 180 citations.

Star, left-star, and right-star partial orders in Rickart ∗-rings

Abstract: Let be a unital ring admitting involution. We introduce an order on and show that in the case when is a Rickart -ring, this order is equivalent to the well-known star partial order. The notion of the left-star and the right-star partial orders is extended to Rickart -rings. Properties of the star, the left-star and the right-star partial orders are studied in Rickart -rings and some known results are generalized. We found matrix forms of elements and when , where is one of these orders. Conditions under which these orders are equivalent to the minus partial order are obtained. The diamond partial order is also investigated.

Monotone transformations on B(H) with respect to the left-star and the right-star partial order

Abstract: Let H be an infinite dimensional complex Hilbert space, and let B(H) be the set of all bounded linear operators on H . In the paper equivalent definitions for the left-star and the right-star partial orders on B(H) are given and bijective additive maps on B(H) which preserve the left-star or the right-star partial order in both directions are characterized. Mathematics subject classification (2010): 06A06, 15A03, 15A04, 15A86.

Minus partial order in Rickart rings

Abstract: The minus partial order is already known for complex matrices and bounded linear operators on Hilbert spaces. The notion is extended to Rickart rings and it is proved that this relation is a partial order. Some well-known results are generalized.

On partial orders in Rickart rings

Abstract: We consider the generalized concept of order relations in Rickart rings and Rickart -rings which was proposed by Semrl and which covers the star partial order, the left-star partial order, the right-star partial order and the minus partial order. We show that on Rickart rings the definitions of orders introduced by Jones and Semrl are equivalent. We also connect the generalized concept of order relations with the sharp order and prove that the sharp order is a partial order on the subset of elements in a ring with identity which have the group inverse. Properties of the sharp partial order in are studied and some known results are generalized.

A Course In Functional Analysis

Abstract: Thank you very much for downloading a course in functional analysis. As you may know, people have look numerous times for their favorite books like this a course in functional analysis, but end up in harmful downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they juggled with some harmful virus inside their desktop computer. a course in functional analysis is available in our book collection an online access to it is set as public so you can get it instantly. Our book servers spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the a course in functional analysis is universally compatible with any devices to read.

Star, left-star, and right-star partial orders in Rickart ∗-rings

Abstract: Let be a unital ring admitting involution. We introduce an order on and show that in the case when is a Rickart -ring, this order is equivalent to the well-known star partial order. The notion of the left-star and the right-star partial orders is extended to Rickart -rings. Properties of the star, the left-star and the right-star partial orders are studied in Rickart -rings and some known results are generalized. We found matrix forms of elements and when , where is one of these orders. Conditions under which these orders are equivalent to the minus partial order are obtained. The diamond partial order is also investigated.

Homomorphisms on Lattices of Continuous Functions

Abstract: This paper deals with lattices of continuous functions and their homomorphisms, with emphasis on isomorphisms. As usual, we write C(X) for the lattice of all real-valued continuous functions on a topological space X with the order induced by that of R, that is, f ≤ g meaning f(x) ≤ g(x) for all x ∈ X. The sublattice of bounded functions is denoted C∗(X). Until further notice X and Y will denote compact Hausdorff spaces. Suppose we are given an isomorphism T : C(Y ) → C(X), that is, bijection satisfying T (f ∨ g) = Tf ∨ Tg and (this is equivalent for bijections) T (f ∧ g) = Tf ∧ Tg. What can be said about T? In particular, how to represent it? We emphasize that T is not assumed to be linear. As far as I know, these problems were first considered by Kaplansky in his venerable oldies [16] and [17]. In the former he showed that if the lattices C(Y ) and C(X) are isomorphic, then X and Y are homeomorphic. The proof is of Stonian style and proceeds by duality (the points of X are identified as equivalence classes of prime ideals of C(X), a prime ideal being the kernel of some homomorphism onto the lattice {0, 1} and so on; see also [2, pp. 227–228] and [23, pp. 129–130]). The papers [14, 24] contain extensions to noncompact spaces. The sequel [17] studies continuity properties of isomorphisms. For instance, it is proved that, referring to the usual sup norm topology, T is continuous if and only if it admits a representation as Tf(x) = t(x, f(τ(x))) (f ∈ C(Y ), x ∈ X),