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REMARKS ON 2-INNER PRODUCTS

REMARKS ON 2-INNER PRODUCTS DEMONSTRATIO MATHEMATICAVol. XVIINo J1984Siegfried Gähler, Aleksander MisiakREMARKS ON 2-INNER PRODUCTSLet L be a linear space of dimension greater than 1·A 2-inner product on L ( [ l ] , [ 4 ] ) i s a r e a l function ( . , · ! · )on L*LxL with the following properties:1. ( a , a l b ) > 0 , & 0 i f and only i f a and b are linearlydependent,2. (a,a|b) = (b,b|a),3. (a,b|c) = ( b , a | c ) ,4. ( a a , b l c ) * a ( a , b | c ) for every r e a l α ,5. (a + a' , b l c ) * (a,b|c) + ( a ' , b | c ) ·( L , ( . I . ) ) i s called 2-inner product space or 2-pre-Hilbertspace. The concepts of 2-inner produot and 2-inner productspace are 2-dimeneional analogs of the conoepts of inner product and inner produot space. Let ( · , · ! . ) be a 2-inner producton L. From [ l ] , lemma 2, we know that(1)(a,biro) = r 2 ( a http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

REMARKS ON 2-INNER PRODUCTS

Demonstratio Mathematica , Volume 17 (3): 16 – Jul 1, 1984

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Publisher
de Gruyter
Copyright
© by Siegfried Gähler
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1984-0309
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XVIINo J1984Siegfried Gähler, Aleksander MisiakREMARKS ON 2-INNER PRODUCTSLet L be a linear space of dimension greater than 1·A 2-inner product on L ( [ l ] , [ 4 ] ) i s a r e a l function ( . , · ! · )on L*LxL with the following properties:1. ( a , a l b ) > 0 , & 0 i f and only i f a and b are linearlydependent,2. (a,a|b) = (b,b|a),3. (a,b|c) = ( b , a | c ) ,4. ( a a , b l c ) * a ( a , b | c ) for every r e a l α ,5. (a + a' , b l c ) * (a,b|c) + ( a ' , b | c ) ·( L , ( . I . ) ) i s called 2-inner product space or 2-pre-Hilbertspace. The concepts of 2-inner produot and 2-inner productspace are 2-dimeneional analogs of the conoepts of inner product and inner produot space. Let ( · , · ! . ) be a 2-inner producton L. From [ l ] , lemma 2, we know that(1)(a,biro) = r 2 ( a

Journal

Demonstratio Mathematicade Gruyter

Published: Jul 1, 1984

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