no you can not get FULL unemployment benefits if you work part-time.
Every month when you fill in the benefit form ("dagpengekort") on your A-kasses's website, you are obliged to provide information about the hours you have had work. The A-kasse will deduct the hours from the unemployment benefits you get for the month in question.
CA A-kasse has made a video in english explaining how to fill in the benefit form. You can find it here:
You ask about possibility to get FULL unemployment benefits - so maybe you are aware that when having part time job you can get Supplementary unemployment benefits.
For being eligible for Supplementary unemployment benefits you must fullfill the same generel requirements as one who gets full benefits. This means you must:
There are specific rules and requirements for getting Supplementary unemployment benefits, and we recommend you to ask your A-kasse about what specific documentation you must provide to them when applying for Supplementary unemployment benefits.
For instance you need a "frigørelsesattest". A frigørelsesattest is your employer's signature that you have no notice of termination in your employment. So you will be able to take full time job with 1 days notice.
Supplementary unemployment benefits in one month are calculated according to the relationship between the member's working hours in the month and 160.33 hours.
When a member who works part-time for a period of 30 weeks in total within the last 104 weeks have received supplementary unemployment benefits, the entitlement to supplementary unemployment benefits expires.
Minimum amount before the A-kasse will pay benefits
The A-kasse must pay a minimum of 14.8 hours to you for a whole month. If you work more than 145.53 hours a month, you will not receive unemployment benefits that month.
Possibility for extension of period up to 12 weeks
Since 1. of january 2017 it has been possible to extend the 30 week period with up to extra 12 weeks with Supplementary unemployment benefits.
1 month with more than 146 paid working hours, entitles to another 4 weeks, where the member can work in a limited period and at the same time receive supplementary unemployment allowance.
Possible to earn a new period of 30 weeks
If you have lost your eligibility for supplementary benefits and would like to become eligible again, you must have reported more than 146 hours a month for 6 months within a 12-month period.