In mathematics, especially operator theory, a paranormal operator is a generalization of a normal operator. More precisely, a bounded linear operator T on a complex Hilbert space H is said to be paranormal if:
for every unit vector x in H.
The class of paranormal operators was introduced by V. Istratescu in 1960s, though the term "paranormal" is probably due to Furuta.[1][2]
Every hyponormal operator (in particular, a subnormal operator, a quasinormal operator and a normal operator) is paranormal. If T is a paranormal, then Tn is paranormal.[2] On the other hand, Halmos gave an example of a hyponormal operator T such that T2 isn't hyponormal. Consequently, not every paranormal operator is hyponormal.[3]
A compact paranormal operator is normal.[4]
^Istrăţescu, V. (1967). "On some hyponormal operators". Pacific Journal of Mathematics. 22: 413–417. MR 0213893.
^ abFuruta, Takayuki (1967). "On the class of paranormal operators". Proceedings of the Japan Academy. 43: 594–598. MR 0221302.
^Halmos, Paul Richard (1982). A Hilbert Space Problem Book. Encyclopedia of Mathematics and its Applications. Vol. 17 (2nd ed.). Springer-Verlag, New York-Berlin. ISBN 0-387-90685-1. MR 0675952.
^Furuta, Takayuki (1971). "Certain convexoid operators". Proceedings of the Japan Academy. 47: 888–893. MR 0313864.
and 25 Related for: Paranormal operator information
mathematics, especially operator theory, a paranormaloperator is a generalization of a normal operator. More precisely, a bounded linear operator T on a complex...
guide or tour operator who is often a member of a local ghost-hunting or paranormal investigation group. Since both the tour operators and owners of the...
of operators that include normal operators are (in order of inclusion) Hyponormal operators Normaloids Paranormaloperators Quasinormal operators Subnormal...
BAY-gənz; born April 5, 1977) is an American paranormal investigator, actor, television personality, museum operator, and author. He is the principal host of...
particular, a normal operator) is hyponormal, and every hyponormal operator is a paranormal convexoid operator. Not every paranormaloperator is, however, hyponormal...
biggest mobile network operator and Internet service provider. In his spare time he's also a keen investigator of the paranormal. Gus is initially disappointed...
statements made during such an attempt. The term is commonly associated with paranormal-based consultation given for a fee in such settings as over the phone...
and not the existence of paranormal abilities. In a series of experiments holding fake séances, (Wiseman et al. 2003) paranormal believers and disbelievers...
Destination Truth is an American paranormal reality television series that premiered on June 6, 2007, on Syfy. Produced by Mandt Bros. Productions and...
Innkeepers at the hotel. The film was based entirely around the inn's supposed paranormal activity. "Torrington's Yankee Pedlar owners hire local contractor to...
of a paranormal reality television program who lock themselves in a supposedly haunted psychiatric hospital in search of evidence of paranormal activity...
length of a word or short phrase. Enthusiasts consider EVP to be a form of paranormal phenomenon often found in recordings with static or other background noise...
confirm Winchester's spirituality and poor state of mind. According to paranormal investigators Nickell and Ignoffo these house oddities have simple explanations...
Yvette Fielding. Torevell is mostly known for his on-camera role as a paranormal investigator on Most Haunted and Most Haunted Live! He has been a member...
635 180 "Ghosts!" October 30, 2023 (2023-10-30) Bill and Toony explore paranormal phenomena with real ghost hunters. Featured cartoons : Haunted Mouse (1965)...
broadcaster and author. He was the founder and the original host of the paranormal-themed radio program Coast to Coast AM, which is syndicated on hundreds...
Pearl Curran popularized its use as a divining tool during World War I. Paranormal and supernatural beliefs associated with Ouija have been criticized by...
operation, in parapsychology, a term describing a broad category of purported paranormal effects Operation, a word which represents a grammatical relation (i.e...
Roger. ""Marble Hornets," a YouTube serial. A forsaken indie film meets "Paranormal." All episodes to date". Retrieved 28 January 2014. "Marble Hornets Season...
1960s hunt for paranormal powers". The New Scientist. New Scientist Ltd. Retrieved 26 April 2023. Wiseman, Richard (2010). Paranormality : why we see what...
Encounters" and "Grey Ghost Project" tours. These tours, although focused on paranormal activity, counter many of the legends of the ship, with facts drawn from...
Civil War. Alleged paranormal activity has been investigated by local paranormal groups and a team from the television show Paranormal State. The Tombigbee...
2017. Andy Dehnart (January 30, 2018). "Zachary Quinto investigates the paranormal on History's revival of In Search Of". Reality Blurred. Retrieved June...
thread was a Photoshop contest in which users were challenged to "create paranormal images." Forum poster Eric Knudsen, under the pseudonym "Victor Surge"...
Two Souls as Cole Freeman, a doctor at the United States Department of Paranormal Activity. Hardison was married to American singer Chanté Moore from 1997...
Global Information