For any C-algebra A let A denote the set of all positive elements in A. A state on a unital C-algebra A is a linear functional ω : A → C such that ω(a) ≥ 0 for every a ∈ A and ω(I) = 1 where I is the unit of A. By S(A) we will denote the set of all states on A. For any Hilbert space H we denote by B(H) the set of all bounded linear operators on H . A linear map φ : A → B between C-algebras is c...

In this paper, we establish a common fixed point theorem for pair of quasi triangular α-orbital admissible with an interpolative (φ, ψ)- Banach-Kannan-Chatterjea type Z-contraction mappings respect to simulation function in complete metric space. An illustrative example is furnished validate our main result. Our result extends the M. S. Khan et al. [15]. As application, provide existence soluti...

In this paper, we give a generalization of Hicks type contractions and Golet type contractions in intuitionistic fuzzy metric spaces. We prove some fixed point theorems for this new type contraction mappings on intuitionistic fuzzy metric spaces. These results generalize some known results in fuzzy metric spaces and probabilistic metric spaces. AMS subject classifications: 54A40, 54E50, 54D35

banach contraction principle has been generalized in different spaces by mathematicians over the years. mustafa and sims [18] proposed a new class of generalized metric spaces, which are called as g-metric spaces. in this type of spaces a non-negative real number is assigned to every triplet of elements. many mathematicians studied extensively various results on g-metric spaces by using the con...

Let (M,ω) be a connected, compact symplectic manifold equipped with a Hamiltonian S action. We prove that, as fundamental groups of topological spaces, π1(M) = π1(minimum) = π1(maximum) = π1(Mred), where Mred is the symplectic quotient at any value in the image of the moment map φ. Let (M,ω) be a connected, compact symplectic manifold equipped with a circle action. If the action is Hamiltonian,...

In this paper, we prove some common fixed point theorems for co-cyclic weak contractions in compact metric spaces. Keywords—Cyclic weak contraction, Co-cyclic weak contraction, Co-cyclic representation, Common fixed point.

Let A, B be algebras and a∈A, b∈B a fixed pair of elements. We say that map φ:A→B preserves products equal to b if for all a1,a2∈A the equality a1a2=a implies φ(a1)φ(a2)=b. In this paper we study bijective linear maps φ:I(X,F)→I(X,F) preserving primitive idempotents I(X,F), where I(X,F) is incidence algebra finite connected poset X over field F. fully characterize situation, when such φ exists,...

Proof. Define a map U → μn by u 7→ u/ū; this gives a well-defined map by exercise 2 of homework 5. Compose with the quotient μn → μn/μ 2 n, and denote the resulting map by φ : U → μn/μ 2 n. It is enough to show that ker φ = μnU , since μn/μ 2 n has order 2. Certainly μnU + ⊂ kerφ, since φ(ζu) = [ζ] = 0 in μn/μ 2 n for u + ∈ U and ζ ∈ μn. Conversely, suppose φ(u) = 0 for some u ∈ U : then u/ū = ...

Let E and F be two Hilbert C∗-modules over C∗-algebras A and B, respectively. Let T be a surjective linear isometry from E onto F and φ a map from A into B. We will prove in this paper that if the C∗-algebras A and B are commutative, then T preserves the inner products and T is a module map, i.e., there exists a ∗-isomorphism φ between the C∗-algebras such that 〈Tx, Ty〉 = φ(〈x, y〉), and T (xa) ...