SCIENTIFIC ABSTRACT VEKSLER, A.I. - VEKSLER, B.YE.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001859230013-9
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 98
• Document Creation Date: November 2, 2016
• Document Release Date: September 1, 2001
• Sequence Number: 13
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

TIKSLER, A . I s
HomorDhism between classes of regular operators in X-linnals and
in their competions. Izv.vys.ucheb.zav.; mat. no-1:48-57 160.
(MIRA 13:6)
1. Leningradekiv gosudarstvennyy pedagogicheakir institut imeni
A.I.Gertsena.
(Operators (Mathematics))

VEKSLER, A.I.
Realizability ol" K-lineals. Oib. mat. zhur. ?
4 no.51ll86-1188
S-0 163. (YJRA 16:12)

AUTHOR: Veksler, A.I. SOV/20-121-5-1/30
TITLE: principle in Semi-Ordered Factor Lineals
(0 printsipe Arkbizeda. i faktor-linealakh)
PERIODICAL: Doklady Akademii nauk SSSR, 1956, Vol 121,1r 5,pp 775-777 (USSR)
.ABSTRACT: In close connection to the representations of Kantorovich[Ref 11
and other authors the author proves the theorems Let X be an
Archimedean K-lineal, lot N be its normal sublineal. In order
that the factor lineal X/N is Archimedean it is necessary and
sufficient that tha following condition is aatisfiedt Let xnE H,
X
> .1v2,...), let the sequence {x The bounded in X. Let
e
'
Is
n
?~ 0 and -A
--x.O. If then OAx4y in valid for xCX and every
n
n
x
y being an upper bound of the aet f?~
j , then zC-N.
n
n
Further five theorems give simplifications of this condition for
special types of K-lineals.
Th~T* are 4 referencest 3 of which are Soviet, and 1-French.
ASSOCIATIONsLeningradski- gosudarstTennyy pedagogiaheskiy Institut imeni A.I.
Gertsena (Le;ingrad State Pedagogical Institute imeni A.I.Gertsen)
~PRESENTED: April 10, 1958, by P.S.Aleksandroy, Academician
fiUBMITTED: April 10,
1958
-Card 1/1 .

VEKSLER, A.I.-fLeningrad)
Conditions for the applicabil-ity of the principle of Archimedes
in semiordered factor groups and factor lineals. Mat. sbor. 57
no.4;477-492 Ag 162. (MIRA 15:8)
(Groups, Theory of)

VEKSLERI A.I., Gand Phys Vmth Sci -- (diss) "Gertain proble:7z
4ZW,A.-
-!i
of the theovy of voiarordered spaceS." Len, 19~~9, 6 pp (T. n of
10,
hdhacation R371-SR. Lan State Inst in A.I. Gertsen. L.:wxair of
Mathematical analysis) 1~',O copies (11, 34-59, 110)
- 4 -

VEKSLERp A.I. (Leningrad)
~ , - :- . .. I
Linear structures with a sufficiently
1-ideals. Mat. sbor. 64 no.2t2O5-222
large set of maximal
Je 164.
(MIRA 17r9)

88888
S/044/60/000/007/044/058
C111/C222
AUTHORt
TITLEs On f'actor-lineals and vector structures
54
PERIODICALi Referativnyy zhurnal. Mat6matika, no-7, 1960, 157-158
Abstract no.7690- Uch.zap.Leningr.gos.ped.in-ta im.A.I.
Gertsena, 1958, 183, 107-127
TEXTs The author proves the results published in an earlier own paper
(R.zh.Mat., 1950, 4917)- He mentions some simplest properties of
factors which lateron are used for the proof. Finally he proves theorem 7
which relates to the investigation of the question when the factor XIN
of the K-space -11 with respect to its normal subspace N is a K-space too.
Theorems Let X be a K-space, let N be its normal. Then for the fact
that the factor X.-N is e K-space it is necessary and sufficient that it
is an Archimedean K-lineal in which there exists the projection of an
arbitrary element onto an arbitrary component. (the set X0C X is called
a component of the K-lineal X if there exists a set E CX so that X 0
consists of all elements x C-X which are disjoint to E; the projection
Card 1/2

88888
S/044/60/000/007/044/058
On factor-lineals and vector.... C11I[C222
of the element onto a component is defined as in the book of L.V.
Kantorovich, B.Z.Vulikh, A.G.Pinsker "Functional Analysis in Semi-
ordered Spaces" (M.-L.-,Gostekhizdat, 1950) for K-spaces).
[Abstracter's note: The above text is a full translation of the original
Soviet abstract.]
Card 2/2

VEKSLER, A.I.
Effectuation of Archimedean linear K-spaces. Sib. zh,.;r.
3 no.1:7-16 Ja-F 162. (M RA 15:3)
(Topology)

VEKSLERY A.I.
Topological and structural ccvpleteness of normalized and
linear topological stractures. Dokl. AN SSSR W no.2:262-
264 Mr 162. (KIRA 15:3)
L Ioaningradakiy tekstillnyy.inatitut im, S.M.Kirova.
Predstavleno akademikom V.I.Smirnovym.
(Topology)

VZY.SLER. A.I.
Co=leteness and d-completeness of normalized and linear
top*logical structures. Izv. vys.ucheb. zav.; mat. no.3:22-30
162. (MIRA 15:9)
1. Leningradskiy tekstilInyy institut imeni, S.M. Kirova.
(Topology)

VFMLERS A.T.
Linear structures vtth a sufficient set of -zilrjql I-IdealB.
Dokl. AN SSM 150 no.4*715-718 Je 163. (MIRA 16:6)
1. Leningradskiy tekstil2nyy inatitut imeni S.M. Kirova.
Predstavleno akademikom A.I.-Yalltse
(Ideal-s