Quasi normed space pdf

Park 6 did the generalization of the term of quasinormed space, i. Orthogonal bases and a structure of finite dimensional normed linear spaces saito, kichisuke and tanaka, ryotaro, banach journal of mathematical analysis, 2014. An element is an endpoint of if and only if it is an endpoint of for every. Quasibanach spaces of almost universal disposition. Park has proven few properties of quasi 2norm, in 3 m. Pdf sharp triangle inequalities in quasinormed spaces. Generalization of the pecaricrajic inequality in a quasi. Park has generalized the term quasinormed space, i. For more information about quasibanach spaces, the readers can refer to 1.

We calculate the boyd indices for quasinormed rearrangement invariant function spaces with some bounds. A study involving the completion of a quasi2normed space. Quasinorm linear space of bounded linear operators is deduced. Let be a quasipseudometric space and let be a setvalued map.

As the moduli are obtained by taking averages, it is necessary to impose some continuity conditions on the quasinorms. A complete quasinormed vector space is called a quasi banach space. Perhaps, this is the most important obstacle in the progress of normed quasilinear spaces. Stability problems of quintic mappings in quasi normed. Park 8 introduced the term of quasi 2 normed space, furthermore he proved few properties of quasi 2norm. Acikgoz 7 elaborated the procedure for completing the quasi 2normed space. A few pearls in the theory of quasimetric spaces jean goubaultlarrecq anr blanc cpp tacl july 2630, 2011. The quasinormed topological vector spaces are precisely the locally bounded topological vector spaces, cf. The fundamental aim of this paper is to introduce and investigate a new property of a quasi2normed space based on a question given by park 2006 for the completion quasi2normed space. Interpolation of multilinear operators acting between. Inequalities of dunklwilliams and mercer type in quasi. The following theorem proves two inequalities in quasi 2normed space, which are analogies to the inequalities stated in theorem 7.

Also he proved some properties of quasi 2norm and m. Fixed points and stability of icosic functional equation. Consider the family of those isometries f whose codomain is a rational pnormed space. By the aokirolewicz theorem 30 see also 3, each quasinorm is equivalent to some pnorm, since it. An element is a startpoint of if and only if it is an startpoint of for every. Schechtman, asymptotic theory of finite dimensional normed space. The section one contains the introduction, the main. In this paper, an alternative way of proving the quasinormed linear space is provided through binomial inequalities. Generalized quasibanach sequence spaces and measures of.

The pair is called aquasinormed space if is a quasinorm on the smallest possible is called the modulus of concavity of a quasibanach space is a complete quasinormed space. Research article a study involving the completion of a. Isometric composition operators acting on the chebyshev space goebeler, thomas and potter, ashley, involve. Acikgoz have given the procedure for completing the quasi 2normed space and in 1, 4 and 6 are proven few inequalities about quasi 2normed spaces. The superlarge category of quasitopological spaces is a quasitopos although this is not immediately obvious for size reasons in particular, it is probably not a grothendieck quasitopos. Quasimetric spaces outline 1 introduction 2 the basic theory 3 transition systems 4 the theory of quasimetric spaces 5 completeness 6 formal balls 7 the quasimetric space of formal balls 8 notions of completion 9 conclusion. Also, we have showed that the quasi normed linear space admits quasi banach dilation mapping which is a lipschitzian mapping.

Quasicontinuous functions and quasiuniform convergence11 2. In particular, it is a locally cartesian closed category references. Conversely, every locally bounded topology on a vector space is given by a quasinorm. Acikgoz 2 elaborated the procedure for completing a quasi 2 normed space, and in 4 are considered families of quasi norms. Introduction let us first recall some basic facts concerning quasibanach spaces and some preliminary results. Recall that a quasibanach space x is said to be a kspace if whenever z is a quasibanach space with a subspace l of dimension one such that z l is isomorphic to x.

Inequalities of dunklwilliams and mercer type in quasi normed space risto malceski faculty of informatics fon university skopje, macedonia risto. An application to lorentz type spaces is also given. Fixed point theorems in quasi semi linear 2normed space. Generalized ulamhyers stability of an aqfunctional. Recently, a number of results of the local theory have been extended to. The locally bounded space x is locally pconvex, 0 quasi normed linear space is provided through binomial inequalities. Robdera1 1department of mathematics, university of botswana, private bag 0022, gaborone, botswan. In this paper, we define continuity and boundedness of linear operators in quasinormed linear space. Park 9 introduced the term of a quasi 2normed space.

Edwin spanier, quasitopologies, duke mathematical journal 30, number 1 1963. Fixed points and stability of icosic functional equation in quasibnormed spaces 262275. Interpolation of bilinear operators between quasibanach spaces. Interpolation of bilinear operators between quasibanach. The value of doing experiments is that they offer the most clearcut route to testing hypotheses about causes and effects. The fundamental aim of this paper is to introduce and investigate a new property of a quasi 2 normed space based on a question given by park 2006 for the completion quasi 2 normed space. Quasisolution of linear inverse problems in nonreflexive. A quasinorm is called a norm if for all in this case, a quasibanach space is called a. Boyd indices for quasinormed function spaces with some bounds. Sharp triangle inequalities in quasi normed spaces. In this work, after giving the notions of quasilinear dependenceindependence and basis presented.

Banach quasi algebra a,a 0 where a is a vector space and a 0 a algebra and a subspace of a, both of them satisfying speci. Pdf inequalities of pecaricrajic type in quasi 2normed. A vector space with an associated quasinorm is called a quasinormed vector space. Closedness of bounded convex sets of asymmetric normed linear spaces and the hausdorff quasi metric rodriguezlopez, jesus and romaguera, salvador, bulletin of the belgian mathematical society simon stevin, 2006. Quasi norm linear space of bounded linear operators is deduced. In this paper, an alternative way of proving the quasinormed linear space is proved, which provides the various ways for selecting the quasiboundedness constant. Quasisolutions were introduced by ivanov 12,15 as the stabilization of linear illposed problems in normed spaces through a. On the subspace problem for quasinormed spaces mangatiana a. Quasicontinuity of sobolev vector elds on rcd spaces21 references 24 introduction the theory of di erential calculus on rcd spaces as proposed in 9,10 is built. Park 8 introduced the term of quasi 2normed space, furthermore he proved few properties of quasi 2norm.

In this paper, we develop a constructive proof of hahnbanach extension theorem in quasinormed linear space. Finally, we also find an answer for parks question. Is called a quasinormed algebra if the vector space a is an algebra and there is a constant k 0 such that. Hahnbanach extension theorem in quasinormed linear spaces. We can refer to 3,30 for the concept of quasinormed spaces and pbanach space. Bounded linear operators in quasinormed linear space. The quasi normed topological vector spaces are precisely the locally bounded topological vector spaces, cf.