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On Idempotent D-Norms
[article]

2014
*
arXiv
*
pre-print

If this iteration is repeatedly done

arXiv:1303.1284v3
fatcat:j5cdyky54rayjfbnspru4yigcq
*on*the same*D*-*norm*, then the limit of the track is*idempotent*. ... We characterize the set of*idempotent**D*-*norms*. Iterating the multiplication provides a track of*D*-*norms*, whose limit exists and is again a*D*-*norm*. ... Then the limit lim n→∞ x n i=1*D*(i) =: x*D** , x ∈ R*d*, is an*idempotent**D*-*norm**on*R*d*. Proof. We know from Poposition 4.2 that ·*D** is a*D*-*norm**on*R*d*. ...##
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On the norm of an idempotent Schur multiplier on the Schatten class

2004
*
Proceedings of the American Mathematical Society
*

We also give a simple characterization of those

doi:10.1090/s0002-9939-04-07340-x
fatcat:qz6aobvd5jbnhndar6ousg2brm
*idempotent*Schur multipliers*on*S p whose*norm*is 1. ... We show that if the*norm*of an*idempotent*Schur multiplier*on*the Schatten class S p lies sufficiently close to 1, then it is necessarily equal to 1. ... Introduction We study*norms*of*idempotent*Schur multipliers defined*on*the Schatten p-class with 1 < p < ∞, p = 2. ...##
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Flat ideals in the unit interval with the canonical fuzzy order
[article]

2018
*
arXiv
*
pre-print

A characterization of flat ideals in the unit interval with the canonical fuzzy order is obtained with the help of the ordinal sum decomposition of continuous t-

arXiv:1801.06060v1
fatcat:ebgjmqvovbcrhnqop4lgzjhpju
*norms*. ...*idempotent*then c = c + = c − . • For each non-*idempotent*element c, the restriction of &*on*[c − , c + ] is either isomorphic to the Lukasiewicz t-*norm*or to the product t-*norm*. ... As an immediate corollary of the above proposition we obtain that if & is a continuous t-*norm*and a, b (a < b) are*idempotent*elements of &, then the restriction of &*on*[a, b] is a continuous t-*norm**on*...##
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Page 73 of Mathematics Magazine Vol. 12, Issue 2
[page]

1937
*
Mathematics Magazine
*

As above but with (c+e)(

*d*+/f)=1 The nilpotent is —(c+eitj III.*One**idempotent*, two nilpotents. 0 ci+dj et+fj 0 The*idempotent*is (c+e)i+(*d*+f\j (c+e)(*d*+f) ... Three*idempotents*, no nilpotents in the algebra. t ci+dj eit+fj j c+exlxd-+f, (c+e)(*d*+f)#1 The third*idempotent*is (l—c—e)i+(1—*d*—f)j 1—(c+e)(*d*+f) II. Two*idempotents*,*one*nilpotent. ...##
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Page 73 of Mathematics Magazine Vol. 12, Issue 2
[page]

1937
*
Mathematics Magazine
*

As above but with (c+e)(

*d*+f) =1 The nilpotent is —(c+e)i+j III.*One**idempotent*, two nilpotents. 0 ci+dj ei+fj 0 The*idempotent*is (c+e)i+(*d*+f)j (c+e)(*d*+f) ... Three*idempotents*, no nilpotents in the algebra. t ci+dj ei +f j c+ex1lxd-f, (ct+e)(*d*+f)#1 The third*idempotent*is (l—c—e)t+(1—*d*—f)j 1—(c+e)(*d*+f) II. Two*idempotents*,*one*nilpotent. ...##
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A note on reduced Jordan algebras

1968
*
Proceedings of the American Mathematical Society
*

The set of values QoiAa) = -Qe2,e,iA23) of Qo

doi:10.1090/s0002-9939-1968-0227241-2
fatcat:75nbg2nvsfbgrh3uv6ublzcuze
*on*AM is called the*norm*class of ei, and is denoted by A(eO. ... Consequently, Witt's theorem implies that the*norm*forms A and N' of*D*and*D*' are similar. Then*D*and*D*' are known to be isomorphic (see[l]). ...##
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A Note on Reduced Jordan Algebras

1968
*
Proceedings of the American Mathematical Society
*

The set of values QoiAa) = -Qe2,e,iA23) of Qo

doi:10.2307/2035351
fatcat:yii5aulni5gjlokvc3fzjbn7ce
*on*AM is called the*norm*class of ei, and is denoted by A(eO. ... Consequently, Witt's theorem implies that the*norm*forms A and N' of*D*and*D*' are similar. Then*D*and*D*' are known to be isomorphic (see[l]). ...##
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A note on involution rings

2009
*
Miskolc Mathematical Notes
*

As an application, von Neumann regular involution rings with central

doi:10.18514/mmn.2009.206
fatcat:5fj7iayxo5cjlbm3b5vym5eaae
*idempotent**norm*elements are described. ... The structure of certain involution rings in which the*norms*are multiplicatively generated by nilpotents is also determined. ... If R is a von Neumann regular involution ring with central*idempotent**norm*elements, then R is isomorphic to a subdirect sum of involution rings R i .i 2 /, where each R i is*one*of the following: (i) ...##
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Locally $B\sp{\ast} $-equivalent algebras

1972
*
Transactions of the American Mathematical Society
*

Therefore |-|2 is a complete

doi:10.1090/s0002-9947-1972-0296704-1
fatcat:rulqstsexbgphcpoybyk35prye
*norm**on*(l-e)Af. But eAf is finite*d*;r. ^nsional, hence complete. Therefore Af=eAf® (1 -e)Af is si Hubert space. We denote the Hubert space Af by Jif. ... Assume that*D*is a *-subalgebra of A, and that there exists K> 0 such that Kv(t) ä || 11| for all t e Ds. Then*D*is B*-equivalent. Proof. * is symmetric*on*A by Proposition 2.1 (3) . ...##
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Norm one idempotent cb-multipliers with applications to the Fourier algebra in the cb-multiplier norm
[article]

2008
*
arXiv
*
pre-print

We characterize the

arXiv:0806.4643v2
fatcat:qfuclqaqn5fv3orupytunspp6i
*norm**one**idempotents*in M_cbA(G): the indicator function of a set E ⊂ G is a*norm**one**idempotent*in M_cbA(G) if and only if E is a coset of an open subgroup of G. ... (We can even slightly relax the*norm*bounds.) ... Hence, every*norm**one**idempotent*in M cb A(G) is a*norm**one**idempotent*in MA(G). By [Boż] , M cb A(F 2 ) MA(F 2 ) holds, and-as M. ...##
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Regular left-continuous t-norms

2008
*
Semigroup Forum
*

The next part is preparatory; we discuss certain systems of continuous and

doi:10.1007/s00233-008-9103-3
fatcat:xdknnpniyzeyjjsr6qju644rme
*idempotent*functions (Section 5). ... The t-*norm*algebras based*on*regular l.-c. t-*norms*generate the variety of MTL-algebras. With each regular l. ... -c. t-*norm*. Then we call ([0, 1] ; ≤, , 0, 1) the t-*norm*monoid based*on*. ...##
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Classification of L^p AF algebras
[article]

2017
*
arXiv
*
pre-print

As background, we develop the theory of matrix

arXiv:1707.09257v2
fatcat:3ueegwlqara5pp43o2ddmbyhbq
*normed*L^p operator algebras, and show that there is a unique way to make a spatial L^p AF algebra into a matrix*normed*L^p operator algebra. ... groups. 2) A B as rings. 3) A B (not necessarily isometrically) as Banach algebras. 4) A is isometrically isomorphic to B as Banach algebras. 5) A is completely isometrically isomorphic to B as matrix*normed*... We don't define hermitian*idempotents*in a nonunital Banach algebra, since whether an*idempotent*is hermitian depends*on*the*norm*used*on*the unitization, even for L p operator algebras, as is shown by ...##
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Idempotents in group algebras

1963
*
Bulletin of the American Mathematical Society
*

(

doi:10.1090/s0002-9904-1963-10926-x
fatcat:xcntjg4uancdnhw325g5rvhpiu
*D*) If ƒ is an*idempotent**on*an abelian group and if ||/|| > 1, then ||/||^>!\/5 [3, p. 72]. (Note that there are no*idempotents*ƒ with jj/ll <1, except ƒ =0.) ... Let us draw attention to the following facts, of which (A) and (*D*) are probably the most striking: (A) If ƒ is an*idempotent**on*an abelian group G, then the support group of f is finite. ...##
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Basic fuzzy logic and BL-algebras

1998
*
Soft Computing - A Fusion of Foundations, Methodologies and Applications
*

by c o n tinuous t-

doi:10.1007/s005000050043
fatcat:dqk53qqlnbawvai7bvpze75p7y
*norms*. ... In Sect. 4 w e*d*e v elop some algebra of linearly ordered BL-algebras. In Sect. 5 we exhibit two additional axioms (B1), (B2) and show soundness and completeness of BL + (B1) + (B2) for t-algebras. ... Continuous t-*norms*We recall some well-known facts*on*continuous t-*norms*. A t-*norm*is a binary operation*on*0 1] (i.e. t : 0 1] 2 ! ...##
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Idempotent, model, and Toeplitz operators attaining their norms
[article]

2021
*
arXiv
*
pre-print

We study

arXiv:2101.03585v2
fatcat:qajo2tfrizhw3krulbrwecpwty
*idempotent*, model, and Toeplitz operators that attain the*norm*. ... Here S_𝒬 = P_𝒬M_z|_𝒬, the compression of the shift M_z*on*the Hardy space H^2(*𝔻*) to 𝒬. ...*Idempotent*Operators It is evident that any orthogonal projection*on*a Hilbert space is*norm*attaining. Here we deal with the issue of*norm*attainment of*idempotent*operators. ...
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