On C₁C₂ symmetric operators

C1 C2- symmetric operators for some types of operators

“…If C1 commutes with A * A and AA * , then A is normal operator. Proof: Since A is C1 C2-symmetric operator, that is A=C1A * C2 (A * =C2AC1 and since A * is again C1 C2symmetric then we have A=C2A * C1 [12]. To show that A is normal operator:…”

“…If C1 commutes with A A * , then A is n-normal operator for each n ≥ 2. Proof: Since A is (n-1) normal and C 1 C 2 -symmetric operator, then we have A * A n-1 = A n-1 A * and A= 𝐶 1 A * 𝐶 2 (A * = C2 A 𝐶 1 and since A * is again 𝐶 1 𝐶 2 -symmetric then also we have A= C2 A * C1 [12]).…”

“…A number of other authors have recently made 𝐬𝐢𝐠𝐧𝐢ficant contributions to the study of complex symmetric operators [7][8][9], which has proven particularly relevant to the study of truncated Τoeplitz operators [10][11]. In [12], authors introduce the class of C1C2-symmetric operators as a generalization of the kind of C-symmetric operators which define as: An operator A ∈ B(ℋ) is called C1C2-symmetric operators if C1 A = A* C2 ( A = C1A*C2), where C1,C2 are conjugations on H .…”

Some Results of Fixed Point for Single Value Mapping in Fuzzy Normed Space with Applications

“…On other hand, functional analysis is one of the most important areas of contemporary mathematics. It plays an essential role In the theory of differential equations, representation theory, and probability, as well as in the study of many different properties of different spaces, such as metric space, Hilbert space, Banach space, and others see [2][3][4][5][6][7][8]. Zadeh [9] presented the ingenious notion of a fuzzy set in his renowned paper, many mathematicians became aware of the myriad possibilities for expanding the classical conclusions in the new fuzzy framework and of their countless applications.…”

Best Proximity Point Results in Fuzzy Normed Spaces

“…One of the most important branches of modern mathematics is functional analysis. It is crucial in the theory of differential equations, particularly partial differential equations, representation theory, and probability, as well as in the study of numerous properties of different spaces such as normed space, Hilbert space, Banach space, and others (Sabri and Ahmed, 2023;Nemah, 2017;Eiman and A.Mustafa, 2016;Zeana and K.Assma, 2016;Dakheel and Ahmed, 2021).…”