scholarly journals Quasiminimal distal function space and its semigroup compactification

1995 ◽  
Vol 18 (3) ◽  
pp. 497-500
Author(s):  
R. D. Pandian
Keyword(s):  
Function Space ◽  
Topological Semigroup ◽  
Mapping Property ◽  
Semitopological Semigroup ◽  
Semigroup Compactification ◽  
Right Topological Semigroup

Quasiminimal distal function on a semitopological semigroup is introduced. The concept of right topological semigroup compactification is employed to study the algebra of quasiminimal distal functions. The universal mapping property of the quasiminimal distal compactification is obtained.

The centre of the second dual of a commutative semigroup algebra

1984 ◽  
Vol 95 (1) ◽  
pp. 71-92 ◽  
Author(s):  
D. J. Parsons
Keyword(s):  
Banach Algebra ◽  
Commutative Semigroup ◽  
Topological Semigroup ◽  
Continuous Functions ◽  
Semigroup Algebra ◽  
Measure Algebra ◽  
Semitopological Semigroup ◽  
Borel Measures ◽  
Second Dual ◽  
Right Topological Semigroup

If S is an infinite, discrete, commutative semigroup then the semigroup algebra l1(S) is a commutative Banach algebra. Its dual is l∞(S), which is isometrically iso-morphic to C(βS), the space of continuous functions on the Stone-Čech compactification of S. This fact enables us to identify the second dual of l1(S) with M(βS), the space of bounded regular Borel measures on βS. Endowed with the Arens product the second dual is also a Banach algebra, so it is natural to ask whether a product may be defined in M(βS) without reference to l1(S). In §4 this is shown to be possible even when S is a non-discrete semitopological semigroup, provided that the operation in S may be extended to make βS into a left-topological semigroup in the manner of, for example, [2] where further references may be found. (Note, however, that the construction there is of a right-topological semigroup.) Having done this we may use results on βS to provide information about the measure algebra.

A construction of a compact right topological semigroup

1994 ◽  
Vol 116 (2) ◽  
pp. 317-323
Author(s):  
Ahmed El-Mabhouh
Keyword(s):  
Free Group ◽  
Topological Semigroup ◽  
Minimal Ideal ◽  
Discrete Semigroup ◽  
Right Topological Semigroup

It is well-known that the structure of βℕ, the Stone—Čech compactification of the discrete semigroup (ℕ, +), is very complex. For example, it has 2c minimal left ideals and 2c minimal right ideals, its minimal ideal contains 2c copies of the free group on 2c generators, see [5], and Lisan[8] proved the existence of 2c copies of the same group outside the closure of the minimal ideal.

Separating Points of βℕ By Minimal Flows

1994 ◽  
Vol 46 (4) ◽  
pp. 758-771 ◽  
Author(s):  
Neil Hindman ◽  
Jimmie Lawson ◽  
Amha Lisan
Keyword(s):  
Characteristic Function ◽  
Topological Semigroup ◽  
Semigroup Compactification ◽  
Enveloping Semigroup ◽  
Smallest Ideal ◽  
Universal Semigroup

AbstractWe consider minimal left ideals L of the universal semigroup compactification of a topological semigroup S. We show that the enveloping semigroup of L is homeomorphically isomorphic to if and only if given q ≠ r in , there is some p in the smallest ideal of with qp ≠ rp. We derive several conditions, some involving minimal flows, which are equivalent to the ability to separate q and r in this fashion, and then specialize to the case that S = , and the compactification is . Included is the statement that some set A whose characteristic function is uniformly recurrent has .

Compact left ideal groups in semigroup compactification of locally compact groups

1993 ◽  
Vol 113 (3) ◽  
pp. 507-517 ◽  
Author(s):  
J. W. Baker ◽  
A. T. Lau
Keyword(s):  
Minimal Ideal ◽  
Locally Compact Group ◽  
Maximal Subgroups ◽  
Compact Groups ◽  
Locally Compact ◽  
Semigroup Compactification ◽  
Continuous Complex ◽  
Complex Valued ◽  
Uniformly Continuous ◽  
Right Topological Semigroup

Let G be a locally compact group and let UG denote the spectrum of the C*-algebra LUC(G) of bounded left uniformly continuous complex-valued functions on G, with the Gelfand topology. Then there is a multiplication on UG extending the multiplication on G (when naturally embedded in UG) such that UG is a semigroup and for each x ∈ UG, the map y ↦ yx from UG into UG is continuous, i.e. UG is a compact right topological semigroup. Consequently UG has a unique minimal ideal K which is the union of minimal (closed) left ideals UG. Furthermore K is the union of the set of maximal subgroups of K (see [3], theorem 3·ll).

scholarly journals Reductive compactifications of semitopological semigroups

2003 ◽  
Vol 2003 (51) ◽  
pp. 3277-3280
Author(s):  
Abdolmajid Fattahi ◽  
Mohamad Ali Pourabdollah ◽  
Abbas Sahleh
Keyword(s):  
Semitopological Semigroup ◽  
Semigroup Compactification ◽  
Enveloping Semigroup ◽  
Semigroup Compactifications

We consider the enveloping semigroup of a flow generated by the action of a semitopological semigroup on any of its semigroup compactifications and explore the possibility of its being one of the known semigroup compactifications again. In this way, we introduce the notion ofE-algebra, and show that this notion is closely related to the reductivity of the semigroup compactification involved. Moreover, the structure of the universalEℱ-compactification is also given.

scholarly journals On the special semigroup “at infinity”

2014 ◽  
Vol 23 (2) ◽  
pp. 131-136
Author(s):  
ABDOL MOHAMMAD AMINPOUR ◽  
◽  
MEHRDAD SEILANI ◽  
Keyword(s):  
Topological Semigroup ◽  
Compact Semigroup ◽  
New Technique ◽  
The One ◽  
One Point Compactification ◽  
Positive Integers ◽  
Quotient Semigroup ◽  
Right Topological Semigroup

This paper presents an important new technique for studying a particular compact semigroup, N∪{∞}, the one-point compactification of positive integers with usual addition, which is an important semigroup. Indeed, the semigroup N ∪ {∞} is constructed as the quotient semigroup of a particular compact right topological semigroup. In the study of such a semigroup, a major role is played by the substructures called standard oids. For instance, some of the already known results on the structure of N ∪ {∞} are obtained as immediate consequences.

On the Use of POCS for Restoring the “Missing Wedge” in Electron Tomography

1990 ◽  
Vol 48 (1) ◽  
pp. 520-521
Author(s):  
Neng-Yu Zhang ◽  
Bruce F. McEwen ◽  
Joachim Frank
Keyword(s):  
Function Space ◽  
Convex Sets ◽  
Electron Tomography ◽  
Spinal Ganglion ◽  
Fourier Space ◽  
Missing Information ◽  
Voltage Electron ◽  
High Voltage Electron Microscope ◽  
Energy Bound ◽  
Spatial Boundedness

Reconstructions of asymmetric objects computed by electron tomography are distorted due to the absence of information, usually in an angular range from 60 to 90°, which produces a “missing wedge” in Fourier space. These distortions often interfere with the interpretation of results and thus limit biological ultrastructural information which can be obtained. We have attempted to use the Method of Projections Onto Convex Sets (POCS) for restoring the missing information. In POCS, use is made of the fact that known constraints such as positivity, spatial boundedness or an upper energy bound define convex sets in function space. Enforcement of such constraints takes place by iterating a sequence of function-space projections, starting from the original reconstruction, onto the convex sets, until a function in the intersection of all sets is found. First applications of this technique in the field of electron microscopy have been promising.To test POCS on experimental data, we have artificially reduced the range of an existing projection set of a selectively stained Golgi apparatus from ±60° to ±50°, and computed the reconstruction from the reduced set (51 projections). The specimen was prepared from a bull frog spinal ganglion as described by Lindsey and Ellisman and imaged in the high-voltage electron microscope.

Finite-order Integration Weights Can be Dangerous

2007 ◽  
Vol 7 (3) ◽  
pp. 239-254 ◽  
Author(s):  
I.H. Sloan
Keyword(s):  
Function Space ◽  
Finite Order ◽  
Small Subset ◽  
Worst Case ◽  
Integration Rule ◽  
Dimensional Lattice ◽  
3 Dimensional ◽  
Sum Of Functions ◽  
Integration Rules

Abstract Finite-order weights have been introduced in recent years to describe the often occurring situation that multivariate integrands can be approximated by a sum of functions each depending only on a small subset of the variables. The aim of this paper is to demonstrate the danger of relying on this structure when designing lattice integration rules, if the true integrand has components lying outside the assumed finiteorder function space. It does this by proving, for weights of order two, the existence of 3-dimensional lattice integration rules for which the worst case error is of order O(N¯½), where N is the number of points, yet for which there exists a smooth 3- dimensional integrand for which the integration rule does not converge.

A Function Space Approach to Spectral Related Problems

2019 ◽  
Vol 10 (6) ◽  
pp. 1220-1222
Author(s):  
T. Venkatesh ◽  
Karuna Samaje
Keyword(s):  
Function Space ◽  
Space Approach
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