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We have X ˜ is a unital Banach algebra with the unit ( 0, 1 ) and called the unitization of X. X ˜ is also Abelian if X is Abelian.
Recall that for a (possibly unital) (mathbb {K} -algebra, the unitization of ({K} -algebra, denothe by (widetilde{{mathcal A}}), is defined to be the unitizationbra linearly isoforphic to ({mathcal A}oplus mathbb {K}), with the prodenotedfined by ((a, lambda ) (b, mu ) = (ab + mu a + lambda b, lambda mu )) for any ((a, lambda ), (b, mu ) in {mathcal A}oplus mathbb {K}).
Then, A # = A ⊕ C, the unitization of A, is a unital Banach algebra which contains A as a closed ideal.
When assessing intercoder reliability of unitization, we reached a Guetzkow's U = 0.17% and the textual conformance of unitization of 91.36% of all coded units.
If A is a unital quasidiagonal C⁎-algebra, we construct a generalized inductive limit BA which is simple, unital and inherits many structural properties from A. If A is the unitization of a non-simple purely infinite algebra (e.g., the cone over a Cuntz algebra), then BA is tracially AF which, among other things, lends support to a conjecture of Toms.
We need to recall the following remark from [4] to give the next result: Let (mathfrak {A}) be a Banach algebra and (mathfrak {A}^) be the unitization of (mathfrak {A}) which is (mathfrak {A}^=mathfrak {A}oplus mathbb {C}) is a unital Banach algebra which contains (mathfrak {A}) as a closed ideal.
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Using the experience of unitizing JAEA-3 for transportability and portability, a general policy of unitization for portability of nuclear emergency response robot systems has been developed.
As unitization hours of generator sets decrease from 4760 to 4115 h/y, the proportion of profits in the income decreased from 12.12 to 4.16%.
Biomass-steam gasification is an efficient unitization technology of biomass to produce gas fuel for a combined cooling, heating and power (CCHP) system.
It can be seen that if X satisfies (A), then so does the unitization X ˜ of X.
Here, using functional magnetic resonance imaging, we investigated the effects of unitization as encoding strategy on retrieval processes in a between-group-design.
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