Sentence examples for The unitization of from inspiring English sources

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.

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.

The unitization rule of every iteration is (sumlimits_{n = 1}^{N} { y_{n}^{k} )^{2} = 1}.) The unitization of final authority score vector and final hub score vector is also needed.

However, very developed porosity could not profit from the sufficient unitization of surface area, due to a weakened interaction between ions and pores wall.

The superior capacitive performance can be ascribed to the porous, conductive and stable LSC framework, the uniform distribution and high mass loading of Ag nanoparticles on LSC, and the effective unitization of redox process.

It can be seen that if X satisfies (A), then so does the unitization X ˜ of X.

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.

The unitization policy would help the robot emergency response team immediately deploy a robot system in response to a nuclear emergency.