The phrase "a unitization of" is correct and usable in written English.
It can be used in contexts where you are referring to the process of making something into a unit or the act of organizing or structuring something into a cohesive unit.
Example: "The project involved a unitization of various components to streamline the workflow and improve efficiency."
Alternatives: "a consolidation of" or "an integration of".
We apply these results to show that C⁎(Cφ,K) and C⁎(Fζ), the unital C⁎-algebra generated by all composition operators induced by linear-fractional, non-automorphism self-maps of D that fix ζ, are each isomorphic, modulo the ideal of compact operators, to a unitization of a crossed product of C0 [0,1]).
Then, A # = A ⊕ C, the unitization of A, is a unital Banach algebra which contains A as a closed ideal.
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.
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}).
If X ˜ is the unitization of a Banach algebra X and Ω ( X ) is the set of characters on X, then the set Ω ( X ˜ ) of characters on X ˜ is equal to { τ ˜ : τ ∈ Ω ( X ) } ∪ , where τ ˜ is defined from τ ∈ Ω ( X ) by τ ˜ ( ( a, λ ) ) = τ ( a ) + λ, for each ( a, λ ) ∈ X ˜, and τ ∞ is the canonical homomorphism defined by τ ∞ ( ( a, λ ) ) = λ, for each ( a, λ ) ∈ X ˜.
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.
Moreover, this is the only way in which a unitization (widetilde{{mathcal A}}) can be algebraically amenable but not properly algebraically amenable, as we will show in Corollary 3.11.
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.
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.
§ 3210.11 Does a lease segregated from an agreement or plan receive any benefits from unitization of the committed portion of the original lease?
However, very developed porosity could not profit from the sufficient unitization of surface area, due to a weakened interaction between ions and pores wall.
