In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.

Let X be a locally finite regular affine building with root system R. There is a commutative algebra A spanned by averaging operators A λ , λ ∈ P + , acting on the space of all functions f : V P → C, where V P is in most cases the set of all special vertices of X , and P + is a set of dominant coweights of R. This algebra is studied in [6] and [7] for˜An buildings, and the general case is treat...

Given a linear map T on Euclidean Jordan algebra of rank n, we consider the set all nonnegative vectors q in Rn with decreasing components that satisfy pointwise weak-majorization inequality λ(|T(x)|)≺w⁡q∗λ(|x|), where λ is eigenvalue and ∗ denotes componentwise product Rn. With respect to ordering, show existence least vector this set. When positive map, shown be join (in order) T(e) T∗(e), e ...

Norm preserver maps of Jordan product on the algebra Mn of n×n complex matrices are studied, with respect to various norms. A description of such surjective maps with respect to the Frobenius norm is obtained: Up to a suitable scaling and unitary similarity, they are given by one of the four standard maps (identity, transposition, complex conjugation, and conjugate transposition) on Mn, except ...

Abstract. Let Fn, n ≥ 2, be the free group with n generators, denoted by U1, U2, . . . , Un. Let C ∗ (Fn) be the full C ∗-algebra of Fn. Let X be the vector subspace of the algebraic tensor product C∗ (Fn) ⊗ C∗ (Fn), spanned by 1 ⊗ 1, U1 ⊗ 1, . . . , Un ⊗ 1, 1 ⊗ U1, . . . , 1⊗Un. Let ‖ · ‖min and ‖ · ‖max be the minimal and maximal C∗ tensor norms on C∗ (Fn)⊗C (Fn), and use the same notation fo...

With a left-continuous t-norm ̄, we may associate the set of its vertical cuts, namely, the set F of functions fa : [0, 1] → [0, 1], x 7→ x ̄ a. Endowed with the pointwise order, with the functional composition, with the constant 0 function and with the identity function, F is an algebra which is isomorphic to ([0, 1];≤, ̄, 0, 1). We characterize the functional algebras arising in this way from ...

in this paper, we deal with molaei’s generalized groups. we definethe notion of a fuzzy generalized subgroup with respect to a t-norm (ort-fuzzy generalized subgroup) and give some related properties. especially,we state and prove the representation theorem for these fuzzy generalizedsubgroups. next, using the concept of continuity of t-norms we obtain a correspondencebetween tf(g), the set of ...

In this paper we have derived four different fuzzy similarities from three extensions of t-norms mentioned in [1] pages 195200. We have derived these similarities in the same spirit like they would have been used in Łukasiewicz algebra. We will present four different similarities based on the extensions of t-norms these are known as Tinf-extension, P-extension, E-extension and Hn extension. Sim...

it is shown that every  almost linear bijection $h : arightarrow b$ of a unital $c^*$-algebra $a$ onto a unital$c^*$-algebra $b$ is a $c^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in a$, all $y in a$, and all $nin mathbb z$, andthat almost linear continuous bijection $h : a rightarrow b$ of aunital $c^*$-algebra $a$ of real rank zero onto a unital$c^*$-algebra...

We treat spectral problems by twisted groupoid methods. To Hausdorff locally compact groupoids endowed with a continuous 2-cocycle one associates the reduced C∗-algebra. Elements (or multipliers) of this algebra admit natural Hilbert space representations. show relevance orbit closure structure unit in dealing spectra, norms, numerical ranges and ε-pseudospectra resulting operators. As an examp...